I have a 2003 4.6 X5 that has the same problem. The wiring harness did not appear to be rusted. After many hours of messing I elected to drill two small holes in the light/trunk button bar. I had to go with two because I had already ran a wire to one side of the metal contacts into the light. There are 4 wires that contact to the bar.

Black/Gray for the left license light
Brown - Power
Yellow/Grey for the Trunk Lid Button
Brown/Gray for the right license light

I tapped into the Brown Power Wire and tied another wire back to the Brown/Gray wire so I wouldn’t have the error display.