Sonoran steel's page has a decent write-up which you may have seen, but the images show the factory wiring diagram which shows which wires control the locker motor.
Retrofit Electric Locker
The problem i think is that when the locker motor is in locked or unlocked position it is cut off from functioning until the proper wiring is connected for the direction it expects to go (i.e. locked -> unlocked) This keeps the motor from over-traveling or running while stalled and reduces the chance of things being damaged over time.
There's also another write-up here that describes how to test the locker motor and this may help you get things moving:
https://www.toyota-4runner.org/3rd-g...ay-quoted.html
This got mine moving without any issues. It may also be possible that your motor is seized and thus will not move without some help. I am not sure the best method to get things moving in that case, but it may be removing the gear cover and manually actuating the locker. You could also remove the motor "can" and move it but be aware that you will have to re-seat the motor brushes which wasn't super easy unfortunately.