It would be really cool to add facial recognition at like 0.5hz to the phone so that it only turns the screen on when you're looking at it. Or alternatively customize the content based on who's present in front of the mirror.
I think the simplest way to do it would be to tie it in directly to your light switch. (Note that the light switch wouldn't be controlling power to the Android device, it would merely be a data signal determining whether the display should be on.)
If you have a window, tying it to the light switch would be ideal. Or you could simply add a small button next to the light switch.