My 95 SC does what you described, not when you turn the key off but when the locks are activated. I have tried swapping a known good module that doesn't do it but I get the same result, so I think it is the lock
solenoids. The module probably senses load on the circuit to know when to stop powering it and if the solenoid is bad it probably won't sense it. The unlocking when turning off is part of...