If the Score Reset relay is pulsing when this happens, check to see if this switch on the 1st Player 1000 Point Score unit is stuck closed, even when the 1st Player 1000 Point Score unit is on zero.

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Are the Coin relay, Game Over relay, and/or Reset relay pulling in when this happens?

If the Reset relay doesn't let go, check these switches to find out which one(s) are keeping it energized. If it's not obvious which one(s) are responsible, you can temporarily disable them with slips of paper between the contacts. The score Drum unit Zero Position Break switches on the 16 score units are a likely suspect so start with them.

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