That's the coiling of the motor of the score motor. (called a "field coil", apparently)

Are you sure you plugged in all the connectors in the head? I have seen this happen in my own collection when I was newer, I forgot to plug in a tiny connector that goes straight from the playfield into the backbox and it did the exact thing you described. I am not sure if Flipper Pool has this plug as that was on a 1970's machine but since then I have seen quite a few machines with the same plug.

Otherwise, you may want to check whatever controls most of the 30 volts to the playfield, clearly you are getting some if the relay bank relays are working (controls the balls) but you are losing it somewhere else. I am assuming this game has a shared fuse between all of it so I do not think that would be it. Dirty tilt relay switch? Weird dirty hold relay issue? I don't think that last thing would allow the pool ball functionality to work, though. But I've seen games where it doesn't care, either, similar to how kickout holes are always live to make sure the ball doesn't get trapped when the game is "dark" (but on), or to make sure the ball kicks out when the game was powered off with a ball in or heading to a kickout hole. So, if that section of circuitry (the relay bank) is not wired to depend on the hold relay, I would check the hold relay. Are your pop bumpers and kickers firing? (I assume so.)