The Start relay may hold itself in until the Score Motor 2B switch opens which is essentially at the very end of the score motor cycle or about the home position. So that could look like the motor is finding the home position on its own while it's really the Start relay that's keeping it running. If you can't get the motor to run when you turn it manually the problem is more likely with your motor runout switch. It could be dirty, or have a loose contact or a cold solder joint, etc.

You can test it with your meter and the game unplugged. Clip one meter probe to the motor service jack (which should be tied to one side of the 1C switch) and the other probe to red-white wire somewhere away from the 1C switch (Start relay switch for example) and set the meter on the lowest resistance setting. With the motor in the home position and the 1C switch open the meter will probably read something over 20 ohms or possibly even open circuit. Once you rotate the motor and the 1C switch closes the resistance should drop to an ohm or less. Does it?

/Mark

Strike my response.

Sounds high. What do you measure if you close the working switch on the Start relay instead? They're wired in parallel so you shouldn't have to move your probes.

I don't have a Golden Arrow schematic but this is from Big Hit earlier the same year.
Big Hit score motor (resized).jpg
Sounds like the wire colors might be the same although beware that the relay switches might not be. If you unplug your game and clip your meter to to the yellow+red and red-white wires your meter will tell you the resistance between those points. The trouble is you can't know what path(s) the meter is measuring. If all the switches are open the meter is measuring the combined resistance of the path through the score motor, transformer, fuse and bounce switch which is probably somewhere between 10 and 50 ohms I'd speculate. If one or more of the switches is closed you should see a resistance of an ohm or less because a lower resistance path is available. The meter still sees and includes the other path in the measurement, but the lower resistance path through the closed switch overwhelms the higher resistance of the path through the motor and transformer.

In this case you can simplify the measurement by disconnecting the motor service jack to take the transformer path out of the equation. Then you're left with just the paths through the various switches. Any one of those switches closing should drop the resistance to an ohm or less and the resistance should be open circuit if they're all open.

Beware that one of those switches is on the AX relay which is an interlock relay. So the switch could remain closed even with the game unplugged since the interlock relay can lock in either position. Check to make sure that the AX relay switch is open.

Once you have the score motor disconnected and an open circuit measured between your probes, you should be able to manually activate any of the relays that have a switch in the circuit (C, G, J, P, etc.) or the score motor to close a switch and the resistance should drop. I suspect that your score motor 1C switch won't drop the resistance measurement as much as the rest of the relay switches because something is going on with that switch. But test several of the switches to compare their resistance measurements.

If you jumpered around a section of wire and that fixed it then the problem could be between the ends of the jumper. The schematic doesn't necessarily reflect the wiring order of the relays or how the daisy chains are done. But any point on the red-white (or any other) wire should be connected equally to any other point on the wire.

Practically though I wonder if perhaps your runout switch has a cold solder joint or some other mechanical issue that makes its connection intermittent. That might explain why jumpering to it (or clamping down on it) helps. It's not very common for a wire to break between the ends.

Late to the show but this may help:

Image 1 (resized).png