Okay, so lets say in the 10th frame you get a spare which gives you an extra shot.
If your 3rd shot in the 10th is a strike, it then doesn't go to Game Over? You get an
extra frame/shot?

Okay, I'm thinking maybe the 10th Frame Unit's wiper board may be slightly off.
In the 10th, if a spare is made, the 10th Frame light may register spare, but another
10th Frame Unit's wiper blade that tells the machine what was made may be slightly touching
another spot up telling the machine a strike was made and there's still two shots to give.
Not saying that's surely it, but the machine would act the way it's acting if it was.
I'd maybe inspect the 10th Frame Unit's wiper along with its board..

Okay. Next I would check the contacts (and solder tabs) in the 1st Shot Relay, but maybe more importantly,
the 2nd Shot Relay. And I believe your machine has a #2 2nd Shot Relay, and if so, I'm thinking the contacts in
that Relay may be the most important to inspect..

Is one of the Frame Unit's wiper blades on that broken rivet when in the 10th Frame?
If so, that could surely be the issue..
The 10th Frame Unit Steps up through the Frame Unit when in the 10th Frame.
When a machine I had in a Tavern lost a rivet, for a quick fix I de-soldered the
wire, filed down the front of the rest of the broken rivet so it would pop out of the
backside, then I put a rather short #4 bolt through the hole and used the nut on the
backside to attach the wire. It remained successful, so I left it to this day..
Oh yes. I would position then tighten the bolt so that the wiper rode with the length
of the #4 head's groove..