So, I felt kind of bad about having to kill the crazy Nightkin in Novac (the one who thinks the Brahmin are talking to him and shoots them to get them to be quiet) - after all, it's not his fault he's crazy - and I decided to see if there was a way to resolve the situation without killing him or letting him go on killing a Brahmin every night. When he did appear the first night, instead of shooting at him directly, I tried to shoot the gun out of his hands, grab it, and then run off with it in the hopes of getting him to just leave. I tried it a number of times, and I honestly can't remember what finally worked, but whatever it was, it resulted in him following me into my hotel room at Novac and then turning non-hostile.

So the Brahmin-killings have stopped and the Nightkin is still alive, but now he just hangs out in my hotel room all day long! Whenever I go back in there, he's still there in cloaked form and doesn't really react to anything, but I can hear him breathing and can see the distortion of the atmosphere from the cloaking. Plus, a couple of times I've heard him say, "Head voices say meat rots in the sun" or something like that, so I guess he's still crazy even if he's not shooting Brahmin any more.

Anyway, I'm sure this is just a glitch and not actually meant to be a way to resolve the quest, but I thought it was pretty funny. It would be great if this was actually incorporated into the closing narration - "Novac prospered under the new regime, though strange stories persisted about a mysterious disembodied voice in one of the hotel rooms...."

That's actually the 'Brooks Tumbleweed Ranch' Nightkin;

http://fallout.wikia.com/wiki/Brooks_Tumbleweed_Ranch

Happened to me as well, I just reloaded a savegame.