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?