I don't have the schematic, but it does sound like this must be AAB (Add a Ball) so in that sense it probably is very similar to the Bon Voyage. The BV also can go up to 9 balls. I have spent a lot of time analyzing the BV (for entertainment) so maybe I might help.
What happens on start-up is a 2-part process which involves the score motor and various switches. (This all happens in parallel with the scores resetting to zero and also other start up things such as advancing the play meter and such).
For the first part, the ball counter is sent from wherever it happens to be sitting down to the zero position, or ball #1. This usually will happen in the first rotation of the score motor, but it will take 2 score motor rotations if for some odd reason the ball count should be at 6 or higher when it starts. But if the ball count happens to be at 1 when you start, then it doesn't need any score motor rotation at all since it is already in the zero position.
It sounds like that part is working OK. You can test it. Manually set it so it has 3 balls, or 4 balls, or whatever, then start it up. It should count down to 1 ball right away.
The second part then adds the balls back on, maybe to 3 balls or 5 balls depending on the machine or the settings. If it counts down to 1 ball OK and stays there and never counts back up, then there is something wrong in this area. On the BV, this circuit is somewhat convoluted but I figured out how it works by carefully observing it. First, it is controlled by a relay called the Game Relay or also sometimes the Game Interlock Relay (which is different than the Game Over Relay), which is actually one of those interlock latch/trip type relays. You should check to see if you have the same. Here is what it looks like.
CR20 CR21 game interlock relay (resized).jpg
If you have the playfield lifted you can watch it. It should be in one position as the ball count goes down to 1, then it should jump to the other position and that makes the circuit that will add the balls back up. So that is the first thing to check. If it never changes position then you won't get any balls added. That is triggered by the Ball Count Unit Zero switch. And that makes sense. That is what I suspect first. This switch is on the ball count unit, and it is a MBB switch, so it should be in one position for any ball count other than 1, and when it gets to 1 it should change position. It is moved by a peg that is on the toothed wheel. Check that switch to make sure everything is proper. You can even test it manually to make sure its working.
SU06 Ball Count Unit zero switch (resized).jpg