Those Who Hunt Elves, while not the first late-night anime, was the one to capitalize on the post-Eva boom when it aired on TV Tokyo at 25:15 on Thursdays (i.e. 1:15 on Fridays) late in 1996. But it wasn’t the only anime to run in that slot – it carried anime for a little over 2 solid years before face4/4 ended up there at the beginning of 1999.
The following shows, in order, were broadcast in this slot from 1996-1998:
Those Who Hunt Elves (Aired 1996-10)
Eat Man (Aired 1997-01)
Hyper Police (Aired 1997-04)
Virus Buster Serge (Aired 1997-10)
Outlaw Star (Aired 1998-01)
Shadow Skill (Aired 1998-07)
In general, I plan on looking into this subject a bit more. The 3/4 years when anime was just going late-night is my favorite period for the medium, and I think it’d be useful to have an easily accessible list of which shows in that period actually came on after midnight (the fact that Master Keaton did while Martian Successor Nadesico didn’t was mildly surprising to me). Probably, this project will involve just making a list of anime broadcast from 1994-2000 and getting all of their timeslots, since the only place I’ve been able to find so far that lists them on show pages is Japanese wikipedia. And doesn’t have pages for many of the actual timeslots, just mentions of them on show pages. It *does* have one for Nihon TV on Tuesdays, though.
And plus, it leads to finding fun trivial stuff, like that before Eva went on TV Tokyo Wednesdays at 18:30, Teenage Mutant Ninja Turtles was in that slot for 2 whole years.