Just to be clear, the rear stepper in this era of Williams games is usually the Coin Unit, which keeps track of the number of players. The spider on the back of it has a lot of fingers on it. The front stepper is usually the Ball Count (or Count Ball) Unit that keeps track of which ball number you're on. It usually has just two fingers. Both bakelite plates confusingly refer to themselves as Player units. It could be different on your game, but it'd be unusual for the time.
The schematic for Pat Hand is here: http://mirror2.ipdb.org/files/1767/Williams_1975_Pat_Hand_Schematic_Diagram_continuous.pdf
As TimMe said, the credit relay should be dropping out on its own after one cycle. It's a little odd that it stops trying to subtract credits after it reaches the zero credit break switch on the credit unit in the backbox. It seems like it should keep trying to deduct credits anyway.
One thing you might try is putting the score motor into service mode and manually rotating it to see just what's triggering/tripping/changing around the game as the score motor advances. There are a few normally closed switches on the score motor that are meant to hold on the credit relay and drop out as it turns, maybe one of them is staying closed.
Cam 5, switch A, in particular, is in series to the Credit Relay. If it stays on, instead of coming open, and the Credit Relay has pulled in once, then the Credit Relay will stay on and never drop out.
Cam 1, switch D is in the circuit that pulses the credit unit reset, which steps down a credit. It should be normally open and close as the score motor runs.