Hi Jason
the "Stevefury video i mentioned": IF (if) You want to learn (everything) about the Start-up Sequence of an "Late Williams EM-Pin" ...
YOUR problem is "when playing" - means: The video is not for to help on Your problem.
Here http://user.xmission.com/~daina/tips/pub/emTips.html - some good tips --- nice to read at a time (?)
Here http://www.pinwiki.com/wiki/ --- a LOT of stuff to read - for EM pins: http://www.pinwiki.com/wiki/index.php?title=EM_Repair
Here http://www.pinrepair.com/ --- a LOT of stuff to read - for EM pins: http://www.pinrepair.com/em/index.htm
Be happy as You have a WELL documented WILLIAMS LATE-EM - the manual cannot write everything (or it would turn out a very thick book).
What did I do - how to start looking-up - narrowing on the problem ?
I read in post-1 "draining (loosing) a ball (enters the Outhole) makes the Bonus-Ladder to be stepped down - BUT NO POINTS are added to the Score-Reels.
I know that the Score-Drums are resetted (stepped forward) with the Help of the Score-Motor and some Reset-Relays. I know that during play: ALL points are given to the Score-Drums THROUGH (pulling) 10-Point-RELAY, 100-Point-RELAY, 1000-Point-RELAY (maybe 10'000-Point-Relay).
So I did look-up the 1000-Point-RELAY in the schematics - I followed the wirings in the schematics - looking out for something with the word "BONUS" - and I found what I show in post-6.
Lets do together what I expect(ed) You to do - http://mirror2.ipdb.org/files/1072/Williams_1976_Grand_Prix_Manual.pdf - page-12 (ori-10) is about "WHERE in the pin is mounted WHAT (relay or stepper)" - Mech. Panel is the bottom board in the cabinet, Playfield is playfield, Insert is backbox, Cabinet is side-wall or back-wall of cabinet, Front door is coin door.
In the JPG I have marked "Ball-Index-Relay" - it is in the (Mech Panel) Cabinet, the Left-Bonus-Relay is on the Playfield, No-1-Star-Relay is on the Playfield.
The manual shows (starting at page-25 (ori-23) all the relays - TAKE FROM MY JPG the COLOR of the wires - look it up (((do You find Ball-Index-Relay-Switch-D, Left-Bonus-Relay-Switch-1B, No-1-Star-Relay-Switch-E))). Investigate on the relays and the switches, greetings Rolf