I was mistaken; its not in UConnect, but a separate button on the overhead console. I never use it, so forgot where it was, my apologies. This button shuts off all the lights (or at least most) that come on when you open/close the doors, including the ones in the bottom of the mirror. It has a little orange LED that lights up when its "engaged" (lights off).
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Also, after turning the button off (button LED is off) so that the lights all work, you'll have to open the door again, or close/open again, before the mirror lights will come on.