Hi wschaub
I actually have played in the very late 1960ies such old pins - therefore I bought me one - I love my Ice Revue http://www.ipdb.org/machine.cgi?id=1262 --- I do not yet have a schematics - I am glad it runs.
My goal in / with Your problem is: At least making an acceptable "Work-Around" - the pin is no longer in an arcade-saloon - You behave and do not press the Replay-Button at times "by now - it is just nonsense".
I show the interesting part of Your snippet of schematics. My "red lines" show the path to activate the S-Start-Relay. We see: DANGER --- the stuff is operated by 110 VAC - the 110 VAC can kill You.
So I strongly advice the (I call it) "De Luxe Jumpering": We always use two Jumper-Wires and hold together the free ends "in the open".
Whenever You work on the pin: UNPLUG the main power cord ! Depending on where in the wiring Your 110VAC-Toggle-Switch is mounted: You may toggle-off - BUT THE FUSE HAS STILL 110 VAC !!! - So always unplug the main power cord.
The first jumpering asks the question "When we jumper (bypass) everything on the "Power-Side-Connection to 'Coil on S-Start-Relay' " --- does the S-Start-Relay actuate ?
Have the pin toggled-off and unplugged. Clip-on a Jumper-Wire at "5 Amp Fuse SIDE wire-of-color-black is soldered-on" --- WE WANT THE FUSE in our circuitry (((IF You would use the other side of the fuse for a starting-point for jumpering: You then would NOT have the fuse in Your circuitry)))
(You have the pin toggled-off, unplugged) Clip-on the Jumper-Wire at the fuse and take the other end out (through open Coin-Door) into the open. Lay down the gator-clip of the Jumper-Wire secure - NOT touching metal.
Take a second Jumper-Wire, clip on at "Coil on S-Start-Relay, side-wire-of-color-brown is soldered-on". Take the other end of the Jumper-Wire through the open coin-door out into the open and lay down the gator-clip not touching metal.
NOW plug-in, toggle-on the pin. With one hand You hold the insulation of one Jumper-Wire (NEVER TOUCH the metal gator-clip) and with the other hand You hold the insulation of the other Jumper-Wire. You put together for a moment the two gator-clips (touching) --- question: Does the S-Start-Relay pulls ?
IF (if) "no luck, S-Relay does not pull": Toggle-off and unplug the main power cord. Take an new / other Jumper-Wire and establish "permanent connection" on the return-side --- se my "encircled blue" lines in the JPG --- It might be easyer to clip on at "Coil on W-Relay" (?).
Have the first two Jumper-Wires ready - plug-in, toggle-on and hold together the gator-clips of the first two Jumper-Wires --- question: Doe the S-Start-Relay pulls ?
Please write about the first (and maybe second) test --- depending on Your writing: We do other testing (means You take out the Coil on S-Relay / measure Ohms) --- or we do proceed in looking for the cause of the fault (we look at the rest of my "marked green stuff" in the JPG). Greetings Rolf
aSittin-Pretty-pinside-snippet-Work-01 (resized).jpg