Center controller reported F16 with generator failure who couldn't change frequencies; the Center controllers coordinated with the other facilities and worked the aircraft to landing at its requested airport.

Narrative

I had just come back from break when the FLM (Front Line Manager) asked me to plug in on DXX for [priority handling]. The controller who was working the [priority handling] had just checked out earlier in the day (see my other reporter). Single F16; had a generator failure. I asked the X side if that was the aircraft just west of the data block (which was in coast) on a XXXX code; he said yes. I called ZZZ1 arrival for a manual handoff on the limited at 12000 and told them what the [priority handling] was. As I got off the line; the X side said the pilot wanted 110; so I APREQed that; which was approved; then the pilot asked for lower. The R side gave them 100; but I told him the MIA in ZZZ1's airspace is 107; so he amended it to 110. The pilot said they couldn't go into IMC. When the X side tried to switch them to ZZZ1; the pilot said they couldn't switch frequencies. I called arrival back and told them we had to do relay clearances; so they initially gave us a 250 heading at 110 and told us to expect a visual approach to runway XX. I relayed this to the X side who relayed it to the pilot. The pilot proceeded to bust the altitude (presumably to stay VMC); so I called approach back (at this point they are in their airspace) and asked what their MVA was in that area since it is lower than our MIAs. They said 9900; so I told the X side that (which flabbergasted him; but the FLM backed me up saying this is a common thing in approach); so the X side gave them 9900. I told him he needed to call the airport for the visual approach; but he was unsure which was the airport and which was the NAVAID; so I guided him through that. The pilot got the airport in sight; so I told the X side he needed to clear them for the visual approach to the runway (which we don't do in the area nor do we train); so he did that. I called approach back and told them we needed a landing clearance and wind check; so he got that from the tower; which he relayed to me. I wrote this on the board and started to tell the X side; then realizing that he had no idea how to do that; I offered to issue it on frequency since I've done it before (though it has been over XX years). He said yes; so I plugged in real quick on the X side and issued the clearance; which the pilot accepted. Next I called the TRACON and asked which taxiway the tower wanted us to have the pilot turn onto. They got that info; though the tower was blocking all the taxiways so it wasn't a factor; but we relayed that to the pilot. I believe from there the tower used the light gun and towed them off the runway (at least that is an assumption).Definitely one of the weirder [priority handling] I've ever seen. I'm glad I was the one on the Y side since the X side is a brand new CPC (Controller Pressure Controller).Recommendation: There are some obvious training pieces here. Also; if the weather had been anything but VMC; we would have been stuck. First; there is no ILS to runway XX; but even so; the pilot might not have been able to even fly the instrument approach since I believe they lost all their instrumentation (though I don't believe they said that on frequency). Second; we don't even have the finals depicted anywhere in our area; so even if we were able to vector them for a surveillance approach; we wouldn't have been accurate; and relays from approach to us on a surveillance approach with the five second transmission interval requirement would not have been feasible. Third; no one except for those of us who have worked approach even knows what it is. Granted this is definitely a [priority handling] that was far out of the ordinary; but it does show what could have gone wrong if the circumstances had been slightly different.