The core problem you face isn't powering the camera, it's dealing with the assorted drunkards who will also be taking advantage of the very same garage for the view it offers.

My suggestion is that you park your car up there and mount your camera inside the windshield, near the top but below any tinting that might be there. A wide variety of such gadgets are available (here's a cheap one from Amazon). Be sure to clean your windshield inside and out.