Falcon DA-50 pilot reported an engine failed during cruise climb. As the pilot was diverting a second engine failed; then restarted briefly and flight crew continued to a safe landing.

Narrative

On Day 1; I was contracted to serve as PIC on a Pt. 91 Maintenance Reposition Flight in a Dassault Mystere Falcon 50 aircraft; identified as Aircraft X and Manufacturer Serial Number #XXI arrived at the ZZZ Airport @ XA:43 PM; at the hangar for Company X and found the owner in his hangar.I introduced myself and informed him I was there to fly the Falcon 50; Aircraft X; and he informed me of the status of the aircraft as released for flight. The required entries were made in the electronic records after their having completed a '6-Year Inspection' a '12/24-month Inspection; and that they'd installed 'New Tires and New Brakes'; and he then further stated that a '45-minute test flight' had been completed the day prior; Day 0 and that all systems checks were uneventful and completed Day 0.He went on to inform me the facility in ZZZ1 was going to be 'hanging new engines off another aircraft since these things have 11;000 hours on them'.After reviewing the NOTAMs and weather for the flight; I ordered 600 Gallons of fuel with PRIST to be uploaded into the aircraft and proceeded to complete my Pre-Flight Walk-Around and Inspections.After normal Pre-Departure Procedures; we had an uneventful departure from runway XX and climb for 3;000 ft. (There was a reported issue with our Transponder; and I switched to Transponder #2 and continued.After a couple of controller changes; we were instructed to climb to FL320.Passing through FL290; we were instructed to continue the climb to FL340. It was at that moment ENG 1 failed; illuminating GEN 1 and OIL lights. I notified the PM that I had RADIOS and CONTROLS and requested him to perform the required tasks; he followed SOP for the situation.After a few seconds; I'd decided that a return to ZZZ would be the best choice; rather than continue with the ABNORMAL situation; considering the aircraft had just come from maintenance.I notified ATC of our return to the field and requested VECTORS and ALTITUDE for the return.We were given a 090º heading and descent to 11;000 ft.Passing through FL190; ENG 3 also failed; and a couple of seconds later the FUEL 1; FUEL 3; and LO FUEL lights illuminated.At this point; I declared the loss of 2 ENGINES and requested ZZZ1 initially; but after considering the population in the surrounding area; and not trusting the inaccurate FUEL LEVELS in the FEEDER TANKS; (because of LATE INDICATION AFTER ENGINE FAILURE).I decided to use the altitude I had available with ENG 2 at IDLE to REDUCE FUEL CONSUMPTION to attempt to land at ZZZ2 and minimize the risk to civilians on the ground in the ZZZ3 & ZZZ4 airports' surrounding communities.Upon reaching assigned altitudes lower; we utilized Pilot Control Lighting to activate the Airport Lights at ZZZ2 and search for the airfield.Passing through 3;000 ft.; ENG 2 failed and I announced our condition and that we were 'GOING DOWN'. A pilot on our same frequency was able to relay that last transmission; and I then focused on gliding our stricken aircraft to a landing at ZZZ2.When I leveled off at @1;600 ft. the airfield was visible at out 2 o'clock; and the aircraft was starting to bleed off airspeed from our indicated 215 kts; the #2 ENG relit and afforded me the ability to lower the landing gear and flaps and land uneventfully. The thrust reverser was deployed and then ENG 2 died a few seconds after landing; but I was able to come to a stop on the runway with ZERO DAMAGE to the aircraft.Upon securing the aircraft and regrouping my emotions; I retrieved my flashlight and went to the LAV to remove the carpeting and inspect the Feeder Tank Shutoff Valves. An item we; as flight crew; are not responsible for checking during a normal preflight. It is strictly a maintenance item unless commanded during a suspected fuel leak checklist. We didn't suspect a fuel leak; as there was still 7000# of fuel in the main tanks. I have photographs of the fuel panel; reflecting the fuel loads in both TOTAL FUEL and REAR TANKS; and the maintenance service valves in the lav taken that evening; immediately after securing the aircraft and regrouping.All 3 feeder tank valves were closed; prohibiting the flow of fuel in the main tanks from moving to the feeders; and we had no way of knowing that was the situation until the engines flamed out. As stated earlier; there were zero indications of LO FUEL in the feeders until a couple of seconds after losing the 2nd engine.