Hi austinmgrant
on the upper part of the JPG You see "my drawn brown wires" --- somewhere there the fault is --- wire to the Switch on 3-4-Reset-Relay - the switch - the connecting wire to switch on the Score-Drum - the switch - the connecting wire to the coil.

On the lower part You see the actual wiring in the pin --- wire-common-yellow (muddy-brownish-yellowish) comes to a solder-lug on a switch - then a thin naked/bare wire hops, hops, hops ...

The colors have faded in Your pin - hard to find the right switch. May want to try: Unplug the main power cord (Safety Reasons) - sneak-in a stripe of paper in a switch on the 3-4-Reset-Relay - in-between the contact-points - mechanically the switch can close - but not electrically. Sneak-in eight stripes of paper - all switches shall have such an sneaked-in stripe of paper. Have points on all the Score-Drums of Player-3 and -4. Plug-in, start a game - the motor runs - the pin would like to reset the Score-Drums --- now You pull-out one of the stripes of paper - and a Score-Drum resets. Then pull-out the next stripe of paper - and another Score-Drum resets. And on and on You pull-out.
ONE pulling-out does not make a Score-Drum to reset - THIS is the switch to inspect and its wires - connecting to the switch on the drum - this switch also - and the wire to the coil on the Score-Drum. Greetings Rolf

0Shangri-La-Work-25 (resized).jpg