It sounds like your Ball Count Unit Step Up solenoid isn't firing when it should because the Coin Unit and/or Player Unit either aren't stepping properly, or their wipers aren't making good contact with the contacts as they do step. To get a better idea of how this circuit should work read through this topic:
https://pinside.com/pinball/forum/topic/williams-grand-prix-revival.
The circuit in your game is nearly identical and there is a schematic on IPDB.org for comparison.

/Mark

When player 2 is playing in a 2 player game the path in red has to work to fire the Ball Count unit when the ball drains:
Jolly Roger Ball Count (resized).jpg
In particular, even if you unplug the game, there should a complete circuit (1 ohm resistance or less) from the blue-red wire, through the Player and Coin Units to the red-white wire if the units are working correctly.

It sounds as if the Player Unit might not reach that 2nd position until player 3 is up.

/Mark

Clay goes into a lot of stepper detail on his site at: http://www.pinrepair.com/em/index2.htm#steps

A shorter version is that there are a few things to check:
- The stepper gear and wiper disk should step cleanly and precisely without hesitation or slop. You should be able to press the plunger into either the advance or reset solenoid, then release it an have the spring do all the work of moving the gear and disk to the next position.
- The snow shoe wipers should snap back into position if lifted slightly off the contact board. If they don't travel smoothly through their channels they may need to be cleaned.
- The snow shoes should come to rest in the center of the contacts on the contact board below, not on either side. If they don't the contact board can usually be rotated slightly under the wiper board to get them to line up. Just find the mounting screws, loosen them a bit and rotate the contact board.