Having just spent several days investigating the inner workings of these poorly made mirrors, I'm posting this info in the hope it helps someone else with cherokee KJ/Liberty jeep power folding mirror problems. I found almost zero info on how to repair them apart from one badly shot video on YT which doesn't go all the way to replacing inner gears.
The common issue with them seems to be a worn worm drive on the Mabuchi motor (as used in model trains btw ^^) or else damaged gears.
The gear kits are available on ebay at an exhorbitant price but still better than cost of replacing whole mirror which, if you can get one, run to over £300 each from Jeep agents.
I've shipped two complete mirrors from US suppliers (to here in the UK) which, when they arrived, proved to have no motors inside so no powered fold in facility.
I realised that you can tell by the price if they're actually electric folding mirror as they'll be over $100. Anything priced less is just a shell with 4 way mirror motor adjuster & maybe the heating element.
Taking apart the mirror is tricky so don't try unless your adept at DIY repairs. Worst part is removing the motor mount from the black triangular housing. It's held in by 2 'snap tabs' which have to be levered up at the same time. Once raised enough to loosen the unit slightly, the top retainer then has to be prized apart for final release. Once you've done this, you can release the motor itself (3 screws on top under the round snap cover and 4 torx on the base).
To take apart the tiny chinese made electric motor itself unscrew the torx screws on the base. Once it's open you can quickly see which parts are worn/broken. The trickiest job of all is replacing the worm drive on the motor shaft. I made a makeshift puller and manage to inch it forward enough to get needle nose pliers behind it so I could stop the shaft turning. This allowed me to *very carefully* file off the old gear and replace it with a new alloy one. Obviously if you damage the motor or bend the shaft, you're into buying a new one. My motors aren't marked up with any model ID but apparently
Mabuchi FK280 12v 5200 rpm can be used as a replacement and will run fwd/reverse by changing polarity (what your switch does). These are cheap and easy to find.
Pix of motor gearing disassembly:
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hope this helps!