You may have put it back together wrong in regards to the placement of the wipers.

Do you see that set of leaf switches? And that post that sticks up off the ratchet wheel? Normally, that post should move around until it comes in contact with the switch. If you look at the photo in IPDB, you can see the post comes around from the left and rests on the post. More than likely, this is shown in reset position (Ball 1).

See if opening that switch stops the stepping. If so, you may need to orient the wiper differently on the other side.

Hitting the Reset Coil (the shorter one on top) should cause the wheel to zip all the way back to resting on the leaf switch. the larger coil steps it up one tooth with each ball.

Okay, The Ball Count reset coil will continue to fire (from score motor switch 1A) as long as:
Any of the score reel (Drum Units) zero switches are closed
or if the Ball count zero switch isn't opening.

On the score reels, there will be 3 switches. One will be the one that should close at "9".
The other two should open at "0". One of them provides the pulses to move the reel back to 0. The other one tells the logic that all of these items are at zero.

When all 7 of those switches are open, the Reset Relay should drop out and allow the system to continue.