Sounds like a bit of "Forum R&D" is needed here
FWIW, if you can identify the up and down motor wires behind your A pillar Kick Trims, where they go through to the Door it would be relatively easy to tap into these, and use a suitable Timer Relay or 2 to be triggered from reverse lamps to dip and raise the mirror ........................
Perhaps an electronics whizz could produce a circuit to do this, may be a better option.
The trick / difficulty would be to set the Relays "run times" so the mirror ends up exactly where you want it dipped, and then set up the "return" run time to get it back to normal driving position again
I'd imagine it would take a lot of fiddling with the run times to get it right, and I am not certain it would return the mirror to exactly the same "regular driving" position every time due to other factors that may affect the exact speed that the motor runs at ..................
For example outside temperature and humidity etc etc ................
I have a funny feeling that my S Class and C Class that have dipping mirrors might have Hall Sensors in them, otherwise how does the memory function work ?? I don't know for sure as I've never looked at this in any depth
Will never know unless one of us tries, a cool project for anyone who has the time, which due to running a busy Workshop I don't right now, so for me Mirrors is not a priority atm.
Finding a suitable S / CL / CLK 500 with M113 V8 as a donor Car for my impending V8 Conversion is the main "hobby" priority right now, as the year is flying by and I want V8 power in the R170 before next Summer