My Centipede Cabaret which I just picked up had a ridiculous amount of rust in the trackball mechanism and needed to be replaced. This is a quick look at what is required to replace a trackball in a dedicated Centipede machine.
If you replace your trackball with a "Happ Controls" trackball and it rolls up when rolled down, you will need to to swap the yellow and green wires for it to roll correctly. Learn more about swapping the wires here...
http://www.arcade.grugel.com/switching%20wires%20on%20spinner%20connector.pdf
BONUS:
Inside Ms. Pac-Man (1981 Cabinet)