It's not the easiest job in the world, but you only have to strip off the door card and the mirror trim on the inner side of the door.
There is a master controller built into the window motor and there is a 16-pin connector, to which 2 black wires (amongst others) are attached - they go to pins 5 & 6.
These are the wires that are causing the problem and need replacing, so you need to run another pair from this connector to the mirror.
Beofre doing this though, check for continuity by putting a meter across the mirror end and the controller end, as it'll rule out any other fault.
Cheers,
Mike