*********EDIT - RESOLVED*******
GOT IT! Dirty/misadjusted switch on the Extra Ball relay was the problem.
*********EDIT - RESOLVED*******
Hey all, I was working on my Hot Tip, which had intermittently failed to advance balls/players. I cleaned some switches in the Ball Index and Player Reset relays, along with a couple others. I also reseated a couple connectors, as one wasn't fully inserted. I think it actually worked well for a moment, but then it stopped advancing at all; I'm not sure what caused it.
Sometimes I just plain struggle looking at EM schematics. If anyone's able to point me towards where I should be looking, I'd really appreciate it.