The original thing controls mirror position before and after reverse engagement via an ecu. The module you're referring to also uses a microcontroller.
I've personally thought about it a lot over some years, but didn't actually have time to try and make one myself.
My idea is to go for a solely mechanical system, an actuator triggered by the reverse gear signal input, which when disengaged would bring the mirror back to its original position.
You'll have to do some modifications to the mirror assembly, by keeping the left right up down adjustment motors intact but instead making the mirror mount capable of moving up and down on a fulcrum.
Please note that I am talking about the mount of the glass mirror only and not the whole mirror assembly.
Thus under normal circumstances the mirror would be controlled by its electric buttons but when reverse is engaged the actuator would move the mirror mechanism down and when disengaged a spring could bring it back to its original position, without the need for an ecu to remember the original position of the mirror.
The actuator which you use could be a central locking actuator, or any other motor which has a lever that has a small displacement.
If I had tried this, I'd definitely not experiment on my original mirror but would buy another one and alter it as desired.
Lastly, it's usually only the passenger side mirror that auto tilts in most cars. I haven't seen both mirrors tilting down on reverse.
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