Well, my bet is that the sweeper on the ball unit is out of alignment and is in contact with the same circuit twice, then moves to the next misaligned contact.
Visually inspect the ball unit and see if the sweeper contact is in the middle of the contact on the board, or if it is offset a touch. The diagram is page 14 in the manual.
Use your finger on the coil/plunger to advance the sweeper and observe what it is doing. Work it through all the balls and the reset sequence a few times to learn how it works.
You probably need to advance the sweeper just a touch, or figure out what determine the reset position, like a stop or something.
Most adjustments like this can be done with your hand and should not require any tools. Once you start adjusting these with tools, you need to know what you are doing.