There are a few schematics on ipdb.org for Williams games of that era including '61 Double Barrel, '61 Hollywood and '55 Three Deuces. They seem to have the same basic setup for the score motor like this one from Double Barrel:
Double Barrel score motor (resized).jpg
Typically there are a hand full of switches wired in parallel that can send power to the score motor. Without a schematic or reliable relay labels you have a little extra work to do but nothing crazy.

Essentially you need to find all of the switches that can send power to the score motor. The three schematics I found all have an 80/black wire on one of the score motor terminals and a 74/orange-green wire on the other. If your wiring is clean enough that you can identify wire colors, you need to trace the non-black wire from the score motor to all the switches it goes to. You can do this visually or use a meter with the power off.

Once you've identified the likely switches you can disable each one, one at a time, with a piece of folded paper slipped between its contacts. If you're lucky one of them when disabled will allow the score motor to stop. If that switch is stuck closed somehow you may be done once you've adjusted it to open and close properly. Keep in mind that the switch might be closed at the contacts, or at the solder tabs or shorted in some other way. If however the relay that drives the switch is active and closing the switch you'll need to figure out which relay it is, and what's sending power to it using the same process again.

/Mark

Hi nkuhlman Welcome to pinside!

Clues and answers to most of your questions are on the schematic. I highly recommend you buy one.
http://www.pbresource.com/mansch.html