You need to verify the voltage in the wire RD/WT (red and white) while connected, while operating the system. You undoubtably have resistance in either the power or ground leg. The difference between the voltage in that wire and battery should be only a couple tenths of a volt. You will need to back probe or pierce the wire as you have to test it under loaded conditions. If it does what you think (provide battery voltage and ground) then it will work just like any other source of 12v and grnd.
The blue wire, green wire, and yellow wires represent the control signals. make any of them hot (battery voltage) and the door should unlock. make any of them ground and the doors should lock. The Red/White is unit power and the Brown is the unit ground.
Bosch Master, ASE Master, L1
33 years MB technician