The one from this site. Didn't know it had a github.
But I fished out my old CDs and reinstalled from those, and now it's working. Maybe the GOG version has something to do with that, maybe reinstalling the game somehow helped, not sure. Put in the patch for good measure too.
A major problem is the mouse is incredibly fast in all menus, to the point of being unusable. I think I've encountered this problem in other old games as well. It may be because JAE uses raw input. My DPI is very high.
And lightsaber trails are missing. (Edit: Discovered this is because of SFX Sabers - the blade looks better, but IMO the trails also add to the feel, I can't decide...)
Also, what is the autoexec file for JAE?
And dismemberment doesn't seem to work. (Edit: Found the cause. g_saberRealisticCombat 3 is not enough, you need g_saberMoreRealistic 3 - and cheats enabled)