Sounds like your Coin Unit may not be working correctly. The snippet below is the circuit through the player unit and coin unit (in red) that advances the player unit/ball count during a 4-player game. I've removed the parts that are relevant to resetting the machine and the final ball stuff, since it sounds like those are working correctly.

The 3 moveable connections in green are drawn for a 1-player game on the schematic. On a 4-player game, the coin unit advances 3 more times, and moves those connections down 1 position each time, so that after 3 more pulses, they are moved out of the way completely - not in the circuit any longer - picture those 3 green connectors as open. So in a 4-player game, the player unit should only advance 1 position as it only gets 1 pulse from the Motor 1A switch through the red path.

It sounds like one possibility for your problem is that the coin unit isn't moving that final time, so the coin unit might be staying in the position that it would be in for a 3-player game, allowing an extra pulse to get through the P4F path.

JetSpin PU 3 (resized).jpg

I was thinking about my last post - disregard that score motor sequence chart above - it really only applies to 1- or 4-player games.

When it finishes erroneously advancing the ball count, where do the player reel lights end up?

Does it do anything different on the last ball vs. other balls?

Doublecheck the player unit's bakelite disc and make sure the wiper fingers are stopping right on the rivets and not landing in between them. And after you begin a game, make sure the starting position of the wipers is correct.

Maybe check the player count unit in the cabinet to make sure the contacts are aligned correctly there too. My Fast Draw started doing weird things and I had to clean up that unit, the wiper fingers had gotten sluggish.