When the e38 sedans & e39/e46 sedans & Tourings have weird issues with the tailgate and other seemingly unrelated components...it pays to look closely at the wiring looms that have bundled wires going from the tailgate into the body. As the tailgate or trunk lid opens/closes...it can eventually break/chafe the wires causing shorts.
If nothing else...it would be a place to investigate since it is a place where the lights (rear tail lights) and the tailgate electronics come in contact with each other. Those electrical loom (up near the hinges) carry wiring for all rear lights and tailgate functions through those corrugated looms you can see when you open the tailgate
Examples of what has been found after examining the loom of various BMW trunks & tailgates: