If I understand correctly the Ball Count unit only advances in one player games. If that's the case we know that the path in red is working correctly:
Old Chicago Ball Count (resized).jpg
When you add more players the Coin Unit steps up and the red arrow moves from position 1 into one of the other positions. When that happens the Ball Count will only step up once the Player Unit reaches the same position as the Coin Unit (e.g. player 2 for a 2 player game, player 3 for a 3 player game, etc.). Apparently none of the three paths to the right of the red path works.
I'd start by having a close look at the Player Unit to see if it's taking clean steps, if the wipers are making good contact with the contact rivets, if there are any loose wires, etc. It seems likely that the gray-red wire on the Player Unit isn't reaching any of the contacts for positions 2-4 but it could be other issues too. You may need to break out your meter to see if you can determine if there's a path through the Player Unit in each of its positions. Less likely but also possible is that the paths are broken through the Coin Unit.
/Mark