looks like someone replaced your score reset relay coil by replacing the entire metal frame, so you got the wrong label on it. It's also the wrong coil part number, but it'll work.
the reset relay won't power unless the game over relay has tripped, then it should power and stay powered when the coin relay powers until the score reels are zeroed.
the switch on the lock relay is closed when the lock relay is unpowered, so when you first turn on the game the game over relay should trip at the same time the lock relay is powering. It's a race, but the game over trip coil is slightly higher power and should win every time.
the lock relay stays powered forever, so you need to either turn the power off/on, manually trip the game over relay, or the ball count unit needs to be stepped up and the zero switch closed (red arrow below) for the reset relay to work.
maybe I misunderstand the problem ... is the game over relay tripping during the reset process?
if the lock relay is not powering and staying powered when you turn on the game or the switch on it isn't opening, that will cause the game over relay to trip (daveh said that in post #7)
if it's not the lock relay/switch, then the problem is likely the ball count unit isn't resetting all the way or the zero switch on it is stuck closed. You can verify by sticking a piece of paper between the switch contacts on the coin relay with the yellow and blu-or wires. Looks like the center switch on the stack has those wires.
you'll probably want to clean off the traces on the ball count unit. A green scrub pad and alcohol works. Remove the black stuff. Most people put a thin smear of lube on the traces which helps the wipers reset when the reset plunger is pulled into the coil. What lube to use is preference, but it can't be tacky or it will make the wipers stall. Don't use standard WD-40 as a lube ... anywhere.
you should test all stepper units by manually stepping and resetting them to make sure the wipers whizz back to reset.