Is this happening before or after the reset has completed?

If it before the reset is complete. Check if you have a 1000 pt switch closed that might be trying to add 1000. or cause the 1000 point score to pull. Do you have a schematic snippets for the reset and 1000 pt scoring?

I had this happen on regular play went from 2 to 3. Check the 9/0 leaf switch and make sure the arm is in between the two sets. I had one case where they were both on the same side.

At the time I was working on a single player game.

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If you are looking for frayed wires or solder bomb I would focus on SL-YEL and WH-RED. If they are connected you could see this issue.

When both reels are at 0 no issue.
When 1000 goes 1 no issue (but a circuit is primed for the next 1000).
The next score will cause both to step together.

One way to test. is to have them all at zero and disconnect WH-RED from one 10,000 score reel. and score 1000 points a few times.

This would impact all 4 players because these wires are common to all players.