There's nothing special about the ball trough switch that would behave differently going from the Ball Count zero position to Ball 1 vs. (say) Ball 3 to Ball 4; if the ball trough switch were too close and the unit getting an extra pulse, it would happen at other steps as well.

I would first suggest stepping the Ball Count unit manually (via its advance coil plunger) and see if it steps one at a time from reset to Ball 1, then to Ball 2, etc. With the ball out, can start a game. Then in the backbox manually step the Ball Count unit once and see which Ball in Play lights up (should be Ball 1). This takes the ball trough switch out of the path for the moment, to help isolate.