Powering a dash cam

[Exscotticus]

I'm driving a 2009 Yaris 4DHB. I'd like to install one of those dash cams that mount below the rear view mirror. I searched the forums for ideas on how to power it. I don't want to snake a wire all the way around since part of it would be visible. The idea of snaking another wire through the A or B pillar sounds great, but it's not something I could or would do on my own. I wouldn't mind hiring someone to do it if I could find someone I trust, but I already have bitter experiences hiring "professionals" who screw things up. Finally, my wife doesn't want me to do anything that can't be easily undone.

The solution I have in mind is to take advantage of the fact that there's already wiring to that area to power the dome lights. It's simple to snake a wire from this recessed area to where I need it for the dash cam perhaps six inches away. Although I'm comfortable splicing and soldering, I want to honor my wife's wishes and not alter the car in such a way that I can't return it to the way it was. If someone can help me identify the female connector that's being used, and if I can acquire its male counterpart, plus another female connector, then I can make an adapter that simply attaches to the existing connector, provides the same connector to the light module, plus a third wire that powers the dash cam.