Reverse light strangeness

[M491Cabriolet]

I have a strange little problem and I hope someone can tell me how to fix it. My back up lights were not working. I thought it might be the switch. I tested it by putting the car in reverse and bringing power to the wire in the multi-wire plug at the harness in the rear left of the engine compartment. The lights work, so the switch is fine. So I figured there was no power going to that particular wire. I tested it (the source wire) with a multimeter and found that there is actually good power in that wire. Strangely, however, the moment I plug the wire to the switch in, the source wire seems to go cold. As a temporary work-around, I took the reverse light wire (from memory, green with a red trace(?)) out of the plug, and brought a hot wire to is separately. Hooked up like this, the reverse light work fine. Everything is fine like this because all the lights work, except that it is not "correct". Has anyone else ever run into such an odd problem? I surrender! Thanks for any info or thoughts re.