Ive had a couple of problems with my headlights recently on my 91' Firebird.

One of my motors burned up and the other the gear disintegrated.

Taken out the headlight buckets/frames and disassembled the motors, i had a full spare headlight motor (with housing) so i swapped over the gear and axle from that, and the motor to the burnt one, now i've tried putting them back in and manually cranking they seem fine.

The problem is when connected to power they wont stop, even through the relay on the car, im wondering if there's supposed to be a trigger switch or the relay is supposed to react to the impedance of the motor.

Maybe my relay is shot, or is this a motor issue?

 

Your car doesn't have discreet relays like the early Firebirds had, you have a headlight module (with some relays inside) that does all of the switching in one unit. It's a black box on the firewall in the area of the windshield wiper motor, usually with the word "GUIDE" on it. If none of the wiring has been messed with, your module has gone bad and needs to be replaced. Here is your headlight wiring schematic.......