The fact that the reels stop tells me the logic is functional. The reel spin motor is typical of a Jennings machine. And, there is a delay relay that shuts the motor off, so that might be your problem with the reel motor. Look for the relay, or small PC board with TRIACs on it. I have managed to get a few Jennings machines up and running, the biggest problem being the acid leaching damage from the NICAD battery that was soldered on the boards.
I have 24 Jennings 400 machines on pallets, just waiting for the right time to go thru them....soon I keep saying.