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As far as I know the wiring is hard wired into the motors, so you can t just use your existing wiring
The wires have terminals on the end that plug into the motors, so it is possible to move the wiring from one mirror to another.
I'm not saying they are all this way because I haven't seen all models, but the mirror I took off of a non-power door (1994) had the motors inside and when I connected them to my wiring (1994) they worked. You have to remove the mirror then unscrew the chrome plate to get to the backside of the motors. That's where you can unplug the wires.
Thank you to the OP and those with advice. I read this and realized that my drivers side door mirror shakes because of the 8mm bolt in the inside of the door. That was a simple fix. And all thanks to you all. I love this site.