Cessna 310 pilot reported that both engines failed sequentially after the pilot left the fuel selector on AUX tanks during an approach. Pilot stated that after switching back to MAIN fuel tanks; power was restored in one engine and a single-engine approach was continued to landing.

Narrative

Aircraft X was prepared for and flown on an Avionics Validation flight; after installation of an STEC 3100 Autopilot system. The validation flight was required after installation by the STEC 3100 according to the installation directions to validate operation of the system. This aircraft's POH and instruments are calibrated in MPH as the primary reference.During this flight; the aircraft suffered a dual engine loss-of-power due to fuel starvation. Aircraft was recovered normally.Mission planning was completed; including review of flight requirements; weather; NOTAMs; calculation of take-off and landing data; and planned flight profile. The aircraft POH was reviewed and a flight data/line-up card with critical and operational information for this aircraft from the POH was prepared. Pilot used Twin Cessna Type Group Risk Assessment tools (TTCF FRAT); as well as FAA Handbook H-8083-2 Risk Management and ADM tools for mission planning. Pilot did a complete cockpit orientation using the POH.Fuel was checked during planning. The main (tip) tanks were physically checked and appeared to be 2/3 full; which corresponded with the indicated gauge readings of 200# of fuel; the aux (wing) tanks were also physically checked and appeared to be full to the filler necks; corresponding with the approximately indicated 120# of fuel. The aircraft is placarded at 50 gallons in the main (tip) tanks; approximately 300#; and 20 gallons in the aux (wing) tanks; approximately 120#. Total fuel was planned at 640#; with a 150# reserve (60 minutes of fuel at 65% power - 147pph; 2450 RPM; 20' MP at 10;000'; this is a conservative approach based on a higher power rather than 20'; 2300rpm and 133 pph).Mission planning was based on a 65% power profile; with intermittent use of 75% power; a 160pph fuel burn for the entire was used for calculations; in excess of the 147 pph in the POH for 65% power. Effective flight time was planned at 3.0 hours; based on 490# of fuel available at 160 pph.Preflight was ref the POH; all lights and systems were ops checked. 2 qts of Phillips XC 20W50 oil was added to the left engine to bring oil level to 11 qts (12 qts total). No leaks or abnormal issues were noted in the preflight. Fuel gauges appeared to operate normally with previously stated fuel levels.Engine start and ground operations were normal and in accordance with both the POH and owner supplied checklist(s); additionally; the Pilot referenced additional Twin Cessna Type Association recommended checks and pre-takeoff reviews (Go/No-Go criteria; abort criteria and steps; engine failure on Takeoff steps; etc...).Takeoff was normal at approximately XA15 hours local; with aircraft achieving Go/No-Go check speed early (75% of calculated takeoff speed in under 50% of calculated takeoff roll). Engine indications were nominal; and performance was nominal. Aircraft gear retraction and clean-up was normal. A VFR departure was initiated; climb profile was set to 10;500 and engine and aircraft performance was normal within POH parameters.The working area was visually cleared; with ADS-B monitoring confirmed; and monitoring of Departure frequency for situational awareness. Area work was commenced after clearing turns and referencing the STEC checklist. Fuel at commencement of area work was approximately 180# per side; with mains selected. Area work progressed uneventfully; with normal aircraft and engine performance. Area work took longer than planned; requiring approximately 60 minutes to complete.At approximately XB:20 hours local; an IFR pickup was made with Approach to conduct the remaining flight requirements (A VOR approach; an ILS approach; an RNAV approach). Systems checks were normal; fuel indicated approximately 120# per side; as expected based on preflight fuel calculations and the flight parameters used to that point. 20'; 2300rpm and 130pph was set inbound for cruise.Inbound to the VOR; AUX tanks were selected; the AUX Tank indicator lights illuminated as expected; and the fuel indicators reflected AUX fuel loads of approximately 120#. Pilot used the tank gauge select switch to check MAIN fuel levels; which were also at 120#. Weather was checked using ATIS; showing approached to RWY XX. Pilot executed a check for arrival; and a check to review the approach. Missed approach instructions back to Radar were obtained.The VOR RWY XX approach was flown inbound. Approaching the Final Approach Fix (FAF); Pilot selected MAIN tanks; the AUX tank lights went out as expected; and Mains showed approximately 150# of fuel as expected (excess fuel from the engines cycles into the MAIN tanks from the AUX tanks). Aircraft was configured normally with Gear; 15' flaps; and lights. Pilot conducted a GUMPS check confirming Gas (Mains and adequate fuel); Undercarriage (Three green); Mixture (full rich - Pilot also confirmed EGTs and CHTs in lower range); Prop (prop full forward and matched without prop synch); and Speeds (120 kts on final approach).Approach and subsequent missed approach were normal. Aircraft cleaned up and accelerated normally in all respects. At level off; Pilot selected AUX tanks to continue fuel management and transfer usable fuel to Mains. AUX tanks indicated approximately 115# each side; and AUX tank lights illuminated normally. Mains checked at approximately 130# each side. 22'; 2400rpm and full rich was set. Vectors to an ILS RWY X (opposite direction) were requested and approved; [arrival] and [approach] checks were accomplished as before. During vectors; assigned 7500 until established on the ILS; RPM was reduced to 2100-2150 to reduce speed for approach. On the final vector to final; RPM was increased to 2400 to check and maintain airspeed.On final; outside of the final approach fix; and prior to configuration; with the localizer course aligned; and prior to glideslope intercept (GS live but not descending) the aircraft was being slowed to configuration speed; airspeed was approximately 140 mph (Flap limiting airspeed for 15 flaps is 180; for gear and full flaps 160). Aux tanks were still selected; normal technique is to select mains prior to configuring as on VOR 21. Aircraft was on Autopilot to validate STEC 3100 operation on an ILS.Fuel indications at this time on AUX tanks was 50# right (approximately 10 gallons) and 80# left (approximately 13 gallons). Engines were set at approximately 22' of MP; with RPM approximately 2400; and mixture was still rich from the last approach; and radar pattern operations.At this point; pilot sensed yaw to the left developing. Pilot cross-checked engine instruments and saw left RPM had decreased to 1700 rpm; and left fuel flow was decreasing; Oil temp; oil pressure; and CHT's were all in normal range. Pilot cross checked airspeed and found it decaying but above blue line of 116mph; due to the loss-of-power on the left engine. Pilot notified the passenger (the Avionics Repairman);' We're losing a motor'.The aircraft at this time started to rapidly enter a left wing low; nose low; left yaw attitude.Pilot toggled off the autopilot and yaw dampener; and initiated the single engine loss recovery procedure by simultaneously raising the left wing to a minimum 5' bank to the RIGHT; applying ½ ball rudder trim with rudder pedals; and selecting full power; full prop; and mixture full rich (3-full-forward).The aircraft achieved level flight; and descent was checked; airspeed had decayed from 140 mph to approximately 120 mph; with an altitude loss of approximately 100'; and a heading change of 20' to the left of ILS course.At this point; the right engine suffered a loss of power; with RPM decreasing. The aircraft yawed heavily to the right; with a corresponding rapid right wing drop and rapid nose drop; due to the power loss on the right engine with left engine loss controls input.Pilot checked power-pitch-mixture full forward and leveled the wings. Pilot verbalized 'Pitch to 120' to obtain an airspeed above blue line. At this point; Pilot made a rapid radio call. 'Tower; TA we lost both motors'. Pilot initiated this radio call to notify Approach of the situation; and to initiate an increased level of monitoring; due to the low altitude and surrounding terrain. The call to 'Tower' was in error.Pilot then pitched to maintain flying airspeed above 'blue line'; airspeed had decreased to approximately 110 knots. Pilot regained airspeed of 120 mph; with a loss of 100 additional feet. Pilot simultaneously initiate main.During this time; Approach made a radio inquiry; Pilot requested that they 'Stand-By'Upon selecting the right tank to main; the right engine recovered full power and momentarily drove the aircraft towards a left roll; left yaw; nose down attitude. Pilot initiated a left wing up attitude to counter the forces while simultaneously selecting left tank to main. The right engine recovered full power and the Pilot recovered the aircraft to level; full power flight.Pilot then recovered to 140 MPH; recovered to being on localizer course (from ½ dot right); and to FAF/GS intercept altitude. Pilot did this to ensure operations within protected airspace; and to fully utilize course and GS information for safety.Total altitude loss was approximately 300' during this incident; with airspeed decaying during the loss of the RIGHT engine to approximately 109 mph; below VYse but above best Single Engine ANGLE of climb (108); recommended single engine speed (105) and minimum single engine control speed (86).Total duration of the incident was less than 30 seconds; from first indication until full two-engine recovery.Pilot then notified approach that power had been restored and that the aircraft would continue the approach. Approach switched aircraft to Tower. Pilot initiated a normal configuration for the approach; and flew the ILS - opposite direction to the localizer MDA.Tower asked if Pilot 'required services'; Pilot stated no; power was restored. Tower asked if Pilot would be making the approach a full-stop. Pilot declined; due to the approach being an opposite direction approach; and there being a tailwind. Pilot chose not to accomplish a circling approach due to the lack of daylight; and not having briefed the circling approach.Pilot executed the assigned missed approach back to radar and requested the RNAV RWY XX with a turn in holding. Pilot requested this to allow for a cockpit and systems check in controlled airspace; without rushing; to ensure that all systems were in order.Pilot and Passenger reviewed appropriate checklists and used the time on vectors to ZZZZ1 to run checklists and make initial assessments. Pilot made an initial assessment that the cause of the power loss was likely fuel starvation from the AUX tanks; despite the AUX tanks showing 75# left and 60# right. main tanks at this time showed approximately 150# each side.Pilot ran fuel calculations and determined that sufficient fuel remained in main tanks to permit a normal approach and landing. Pilot checked all CBs and switches; and confirmed all systems appeared to operational and with normal function.With the systems confirmed; Pilot ran [arrival] and [approach] checks for the RNAV RWY XX approach. Pilot requested to proceed directly inbound rather than execute the turn in holding; since the desired systems checks and prep for landing had been accomplished.Approaching the Final Approach Fix; Pilot extended gear; the right main gear was perceived as slow to extend; Pilot checked the bulb; which tested good; and stated; 'We've got a bad gear' to the Avionics Technician; and recycled the gear for a good down-and-locked indication. Pilot may have inadvertently keyed the mic when discussing gear with the Avionics Technician. Pilot reported Final Approach fix with gear for a full stop RWY XX. Approach and landing were uneventful.On shutdown; AUX tanks continued to indicate 80# left (13 gallons) and 60# right (10 gallons); physical check of these tanks showe