... 3" High-Ball Trackball ... Happ....
... assuming that the High-ball model has a similar light mounting configuration to the others. I'm guessing it's the same base, so it probably does....
Yes, all happs 3" TBs use the same part for the bottom half of the case. The old atari 3" TBs should be exactly same too, but I don't own one of these old TBs, so I can't verify it.
FWIW, the only difference is the top half of the base. Well, okay, and the sensor boards, old arcade green vs new arcade red vs USB.