I want to reference this very useful thread on mirror motor repairs. The fix contained there is very similar to what I'm about to detail. This other thread contains instructions for swapping mirror motors.
Removing the mirror is pretty straightforward; remove the tweeter (it pops out with a little persuasion), move the insulation, take the two bolts out. The mirror should come off; then, you can get to the locking ring. Because the vertical axis motor was disconnected, I actually could move the mirror enough so that I didn't have to insert the screwdriver into the small hole in the bottom of the assembly; this helped with seeing what I was doing. However, this also means that when the ring unlocked, the screwdriver continued onward towards my other hand. Now my screwdriver has blood on it.
Taking a look at the top of the motor (above) you can see that the small circular motor gear is supposed to attach to the long, flat gear which is attached to the mirror itself. As the small gear turns, the vertical angle of the mirror changes. You can also see a small channel between the flat gear and the motor housing. The width of this channel changes (albeit minimally) as the horizontal angle of the mirror changes. To my understanding, the flat gear needs to be pushed up against the small gear, but not with too much force; if there is too much force, then the mirror cannot be moved by hand, and, badness will happen when the flat gear reaches the end of its track (it won't be able to "skip").
Below is a diagram I sketched up on the whiteboard.
With no spring-like piece to provide force to hold the flat gear against the motor, the flat gear is completely free to move around. With a little bit of fiddling, you can get the flat gear out. Below you can see the glue marks that held whatever spring-like piece used to be there (it's probably on the interstate somewhere now...).
I considered using this very small torsion spring which I found and extracted (and bent up) from a little alligator clip. I tried to fasten it to the backside of the flat gear, but I couldn't get it to stick well. A more clever craftsman might have been able to make that work.
Instead, I thought that a small rubber grommet or similar would do the trick: it would provide force between the motor housing and flat gear, but not too much that the gear couldn't disengage. I couldn't find a rubber grommet small enough, so I just cut a small piece out of one (the missing bit is what I used):
I did not glue the rubber in but instead just shoved it in there between the engaged flat gear and motor housing (below).
Then, to ensure that the grommet would not escape, I covered the top hole with some of the mangled alligator clip from earlier. I superglued it into place. I think covering the bottom may be useful but superfluous; I think the bottom of the housing is close enough to the back of the whole assembly that the grommet can't escape anyway. I could be wrong...
I then plugged the motor back in to the car and had an assistant help me ensure that the motor would now move (and lock) along the vertical axis. It did, so I patched it all back up.
Also a good time to wash the dirty mirror. Then, reinstall it. Good as new! Well, sort of.
I have a feeling that this fix may not work forever, but it is at least a solution short of locating a working mirror motor. Also it cost something like $0.75 and took about two hours. Most of the two hours was spent trying to get the stupid torsion spring out of the alligator clip, which actually turned out to be altogether unnecessary.
If it turns out my fix starts to fail, I'll update this with whatever improved hackery comes next. Hopefully this post will be useful to someone...
