Okay, I'm using an old trackball out of a Centipede machine and a basic Atari mounting plate.
The holes in the plate are square, which makes me think it's supposed to use carriage bolts. However, I've checked every place I can think of and the smallest diameter carriage bolts I can find are 1/4" which is too big to fit in the holes.
Has anyone come across any smaller than that? I'm not sure what to use now.