On the auto-dimming mirror, the blue wire is the ground and white wire is 12V.

On a BMW it's pretty easy to figure out, typically a brown wire on a BMW is ground, and green wires are 12V power on key position 1, and lavender wires (or light purple, whichever you prefer) are power on key position 2, and blue wires are power when engine is on

After checking into hard wiring my detector, and not wanting to risk breaking the overhead console I found this little item that solved the problem

The wire broke on the first attempt to install

but I guess wires are too cheap