Combine the two answers below. Based on likelihood, the problem is in the failing wiring at the key switch, maybe even the button switch. The wires short, engaging one or both lock relays. Disconnecting the plug under the steering wheel will prove or disprove this, provided you've already blessed your fuses.

Each lock motor has a resettable fuse in the form of a PTC thermistor disc that will allow all of the motors to be powered indefinitely without causing a fire or kicking the fuse panel's fuse. The result will only be a subtle battery drain over night. There won't even be enough current passed to form noticeable resistance to manually lifting or pushing the lock button.