if you stick a voltmeter probe on the black wire ... the one on the 10K reel coil will do ... and stick the other probe on the A-D points damoib marked, you should be able to verify the 24V (or whatever it is on that game) when pulling the 10K reel plunger in.

I woulda guessed the EOS switch on the 10K reel, so jumpering the RED+WH to GR-BLK on the 10K reel and stepping the reel is the last useful jumper.

try resoldering #2.

also jumper A to #2. You should get AAB every time the 10K reel goes from 2 -> 3

jumping A to any number on the decagon board should add a ball when the reel increments from number to number+1.

those thru-hole connectors on the decagon board need a lot of heat to get a good solder joint.