I think your original problem was that you stopped the score motor between home positions. If you rotate it to one of the three home positions with the power off it might start right up. Details at: https://pinside.com/pinball/forum/topic/replay-button-doesn-t-start-a-game-by-design
Yes, the replay button and other "stuff" on the coin door is wired with 120 VAC so don't go poking around there if you're unfamiliar with it.
And yes, the R/Hold relay stays on once the game is turned on.
/Mark