I think displaying the long/lat would be a good thing. Especially if you have these missions in mind. Rescue missions would be awesome.
It's a bit hard to find a good place for it in the HUD though, because in almost all places there's a text or gauge in the way. Mabye the best place for it would be right above the scanner, but I think then it might be obscured with the "xx m/s Relative to something" line if the name there is too long. Or it could go right bellow that line, but then the non-compact scanner would be there right under it.
Also it could disappear after you reach a specific height, just like the axis displays.
Astronomers are using the
Gauss' Method it seems, when they don't know the distance to the object.
Which could be the case if only the signal of a distress beacon is all all you have to work with. You need to measure it's position in the sky at least three times, and the more measurements you have, the more exact the solution will be. In the game, this could be simplified to like you need to maintain a high orbit around a planet for some time, and use a scanner equipment which would do the calculations, and the longer you wait, the better your chances are that the orbit that is shown in the orbit map is precise enough. But maybe if you are waiting for too long, then you won't be able to make it there in time (leaking atmosphere, faulty environment control system, etc). Although nothing would keep you from repeating measurements during flight, so this might not be a real trade-off, not sure. Maybe it's harder to measure this stuff, when you are on an escape trajectory, because a planets location in known to very precise levels, and you can use it as a basis for your measurements.
But if you are close enough to the target, the measurements could become easier and quicker to do.
I'm not sure how realistic this would be, but maybe there could be a preciseness for this measuring, in relation to the distance to the object you are orbiting, then it drops significantly with your distance to the orbital parent, and goes up if you are close enough to the beacon, but if your measurements weren't too good to start with, then you might not get close enough to be able to do measurements fast enough.
Also one would think, the ship/beacon should know it's trajectory, and should broadcast it. Maybe this could be a difficulty factor: some beacons broadcast it, some are not, because it's faulty/damaged enough to not be able to determine it.
Also there was an interesting way of finding two missing astronauts in
Heinlein's The Rolling Stones. The lost astronauts were unable to broadcast too far if I remember correctly. The searchers only had a simple radio loop, which only gave out a tone to the space suit's audio system, which's loudness was directly related to the distance and if you are holding the instrument in the right direction. So they first needed to pick direction (the loop didn't tell if the signal is coming from behind or from in front of it), then go that way. If the signal got stronger, then they picked the right direction, if not then it's problem, because the stranded astronauts had quite limited oxygen supply.
Maybe something like this would be interesting challenge. The mission gives you only the estimated orbit of the ship in distress. No beacon, or only very weak signal (or the above mentioned bad measurements). You go to the location where the ship is suspected (this could be a nav target), then turn on this radio loop, and rotate until you have the strongest signal (maybe a strength bar to show, or even an audio tune. Waveform display eventually, if the new UI comes around eventually.), and then you start accelerating in that direction. If it becomes fainter, then wrong direction, turn around. Interplanetary space is big enough to give enough room for this even with the 100 km scanner range we have right now.
Also in Elite Dangerous, the way you find undiscovered planets if they are too far for your scanner to pick them up. You go pretty fast, and look for parallaxing points of light in the sky (stars that are moving relative to the other ones). If you are close enough the target, but it's above your scanners range, you might be able to look for parallax in the same way (assumed, the engine draws a small point for far ships). Relatively small distances and good relative speed/time acceleration might allow you to do that. Although syncing orbits only on this visual information would be quite hard I think, but maybe if you get close enough, your scanner could have a fix on it and show it above it's range, but the exactness of it would deteriorate with time, so you would need to hurry.
A similar thing could be done to crashed ships too. Like you would need to do some scanning from orbit to be able to triangulate the beacon properly. Maybe even doing it from polar orbit for harder cases.