Cessna 560XL Captain reported a main landing gear malfunction on approach during night conditions. The aircraft landed safely and taxied to the ramp.

Narrative

Our Crew on Aircraft X picked up a family of 8 pax; at ZZZ1. We loaded luggage and passengers and departed for ZZZ. All went well with the flight until outside the final approach fix for the ILS approach to runway XY at ZZZ. I called for gear down" at 1 dot before intercepting the glide slope and just before turning to join the localizer (on a left base to final) as we were on a visual approach; backed up by the ILS approach. My First Officer; always holds on to the gear handle until the expected indications are present on the gear display; and then she will announce the indication. In this case; the announcement was; "gear red unlocked; and only 2 green; the right main gear green light is not on."We immediately asked Approach Control for vectors away from the airport so that we could troubleshoot our issue with the landing gear. Our landing clearance was canceled and vectors were issued. The First Officer pulled the QRH Emergency Checklist for "Landing Gear Will Not Extend ;" we followed the checklist to include slowing the aircraft; pulling the gear control circuit breaker; yawing the tail and; finally; using the emergency gear up-lock release handle and the Nitrogen bottle donut to blow down the gear. There was no change in our display indication for the abnormal position of the landing gear.We discussed multiple scenarios; engaged in further troubleshooting; and reviewed options to remedy our situation. Part of our discussion included the possibility that our bulbs for the R/H Main Gear indicator were blown. But we decided it was not likely that we had 2 bulbs in a single display button burned out at the same time (both of us always check all of our annunciator buttons to make sure that both bulbs are functioning; exactly for this reason). Additionally; if it were simply bulbs burned out for a landing gear indicator; logic says that the Red "Unlock" light should not be on. So we had to assume that the R/H Main Gear was not fully extended and locked; and that an emergency landing with a possible faulty R/H Main Gear was inevitable.I then gave control of the aircraft and radios to the First Officer (on autopilot); as I addressed the 8 passengers in the cabin to brief them on the emergency at hand. They appeared to understand the situation at hand; although no one said a word except for the client. The last thing I said to the passengers was to tighten their seat belts really tight just before touch down just case we did not have an extended R/H Main Gear.Once back in the cockpit with the First Officer; I briefed her on a plan to see if the Tower would let us fly a low pass by them to see if they could verify all three gear down. Then regardless of the outcome of whatever they could see; we would still land the airplane as though we had No right main landing gear available to us.We started by letting Approach know that we would need Fire and Rescue Services immediately available to us upon landing. We then asked for the fly by; which they approved. We were told that the airport was "ours;" and that they would close it completely if needed. All the while; we were closely watching our fuel status as it was down to about 1400 lbs at that point. Our goal was to burn off as much fuel as possible to minimize the magnitude of any potential fire event should the worst case scenario happen upon landing.Approach vectored us onto a right downwind for [Runway] XX so that the Tower would be looking at our right wing (per our request) as we passed by them on a low approach over the runway. We were handed off to the Tower and the low flyby took place with the Tower to our right; and left wing dipped down; for about 3 seconds or so. Then straight and level over the runway in a "go around" configuration; flaps up to 15 degrees but no change in gear down position; climbing to 2;000 ft. An aircraft holding short of the opposite end of the runway stated he would look underneath our airplane to see if he could see all 3 gear down aswe flew over him (to no avail; too dark). As we continued our climb out; the Tower reported that all they could see was something white under the right wing. I told them that their report was encouraging as they could've been seeing the right main gear door (and where the gear door goes; the gear leg should go as well). But in the cockpit; we decided to continue with the presumption that the right main gear was not fully down and locked.As we further continued our climb out to 2;000 ft; a Medivac helicopter on the taxiway commented that they would check with their Company to see if they would permit them flying near us to see if their night vision goggles could assist them in helping us verify where the right main gear was.I continued a very long runway heading outbound with an eventual base turn to join the ILS localizer for [Runway] XY for our final approach to landing. Fuel remaining was about 950 lbs at that point. We decided that no further delay for proceeding with our emergency landing was necessary so as to avoid a possible fuel exhaustion scenario. As we approached the final approach fix; I quickly switched to the cabin intercom to let the passengers know that we would be landing in the next couple of minutes. "Seat belts tight!" Then quickly back to Comm 1.The first Officer ran through the "Before Landing" Checklist. After fully configured for landing and throttles pulled back significantly; we now had the gear warning horn blaring for the rest of the flight. As we started down the glide slope; I could see the helicopter about 1/4 mile from us at our 1 o'clock; opposite direction; moving toward our 2 o'clock. At that point; I cut off the autopilot and dipped the left wing down so that they could see under the right wing. Their report was that they thought they could see a right main gear down; but couldn't verify if it was fully extended. The rest of the approach to landing was hand flown; no autopilot. We continued down the glide slope and leveled off at the runway exactly at Vref.Airplane was banked to the left with the nose on the centerline; the left main tire touched softly; then the nose tire; and then the plane inevitably began settling down with the right wing lowering; in spite of full left aileron deflection with the yoke. I never really "felt" the right main tire touch the runway; but the lowering right wing; thankfully; stopped settling with the aircraft perfectly level; as the right main landing gear was holding us up. Speed Brakes; gentle thrust reverser; and gentle brakes; all on the centerline. The rollout was accentuated with multiple callouts by me and the First Officer; "Thank You; God;" Thank You; Lord!" The final one by me saying; "Although neither one of us on this plane deserve this; Thank You; God; for protecting us all."From this point on; our taxi was slow and deliberate; very slow turns in case the right main gear was not locked down; gear warning horn still blaring; final fuel remaining at 850 lbs. The Tower asked if we needed the Fire Trucks to follow us in to the ramp. I replied "yes; in case the right main landing gear collapses."Upon pulling into the chocks; I cut off the throttles (APU was already on); then the first Officer instinctively silenced the Red Master Warning and the Yellow Master Caution buttons simultaneously. At that moment; the gear warning horn finally silenced. Then; a few moments later; the First Officer noticed that the Right Main Gear indicator light had turned on; "three green; no red;" as the Red Unlock light had finally extinguished.Local authorities greeted us at the open cabin door to make sure we were all ok. Passengers all disembarked; appearing seemingly relieved; and grateful; for the benign ending to our Emergency Landing. Three luggage carts later; all the passengers' luggage was in the FBO with them; awaiting a ride to the hotel; as was being arranged per our company.By the way; you could tell that every one of our senses (as an Emergency Landing Crew) were totally peaked and on full alert; because although it was pitch black in the night as I stood at the bottom of the stairs to "catch" each passenger if they were to stumble while exiting the airplane; I literally saw a 4mm object which appeared to fall from the wife's upper torso area to the black asphalt below. Once she completed her final step onto the asphalt; I announced to her that it looked like she had just lost a pearl. I bent over to pick it up for her and discovered that it was a pearl stud earring; of which she was only wearing 1. Then I told her that all we needed to do now was to find the backing clasp for her stud earring. She stated that it would be impossible to find since it was so tiny. I quickly ran up the cabin door stairs to ask the first Officer to keep an eye out for the earring backing; and there it was on the passenger's seat (and it looked "huge" from the main cabin door entrance…amazing what adrenaline can do to our senses in an emergency). I feel like that was a bright spot for the wife; and a nice way to end what was nearly an hour of uncertainty for our passengers.I then spent the next couple of hours debriefing with the Assistant Chief Pilot and Chief Pilot on a conference call; and then with the Lead Mx Controller; maintenance write-ups; and then a thorough post flight inspection and putting the airplane to bed. Way before then; the first Officer had already thoroughly cleaned the interior of the plane to "look like new" status.All in all; a great ending to a challenging in-cockpit emergency; the likes of which neither one of us have ever trained for specifically. But thanks to the extensive training we have received; and continue to receive on a regular basis; it certainly did prepare us to rationally and thoughtfully work as a team to logically and professionally prepare our emergency landing for the best possible outcome; whether the gear was down or up. We are; indeed; grateful for the superb level of training which the company provides to us all. I am; personally; grateful for the incredibly smart; level-headed and thoughtful professionalism of my Co-Pilot; who I am honored to have been seated next to that night. She was spot-on; and on the same page as me; every step of the way. We worked extremely well together as one cohesive unit. For all the professionalism she demonstrated that night; I am immensely thankful. And; most importantly; I am thankful for the gifts with which God has blessed me and the First Officer in order for us to be able to deal with an unrehearsed emergency such as this in such a calm; step by step; protocol-driven manner; which resulted in the safety and security of 10 souls that night. Ultimately; I give the glory to God for providing us with a hedge of protection which only He can provide in the safe deliverance of the 10 souls in our airplane that night. In doing so; He also helped us to preserve the rapidly increasing eminence in reputation of the Company we so proudly serve.In talking with our Lead Mx Controller and with the First Officer; I feel like the best way to prevent what happened on this leg would be to consider a proactive Mx approach to addressing whatever issue was the culprit for our false negative failure indication. Whether it's a dirty; faulty main landing gear micro switch type sensor; or some other cause; it would be great to regularly schedule detailed checks of these micro switches/sensors; or whatever the culprit was; in the end. In discussing our gear indication fault with one of the mechanics looking at our plane a couple of days later; it sounded like this plane had a brand new down-lock actuator installed on the R/H Main Gear about 9 landings (16 hours) prior to our emergency landing event. And this actuator has a micro switch built into it from the factory which I believe is not adjustable (I could be wrong on this). He also indicated that a Maintenance Tech could have damaged the electrical terminal com"