This may be an early warning that your transmission control switch is failing. This is a purely mechanical switch buried under the transmission, part of which controls that back-up lights. It is a clamshell design secured with rivets and the may start to rust out. The result is that some contacts inside the switch may not work properly. I do not want to alarm you unnecessarily, but if everything else ckecks out this is a possibility. Bad news, the switch is ~$600 if you can find it. Good news, you can fix the old switch, by cleaning lubricating and replacing the rivets by 2mm X 8mm screws.
I will look up the wiring diagrams to suggest other reasons for the problem, although my recollection is (I did this 7 years ago) that the circuit is pretty simple and although the switch closes the circuit for the auto mirror controller, they are in parallel, so I doubt RustySpokes's hypothesis, but I may be wrong.