You need a 3rd wire to provide power for the 'parking mode'.

But then I have to find a place for the battery. I always read that keeping lithium batteries stored in a car (with drastic temperature swings--up to 160F in some cases) was bad for batteries?

Nice work! Did this same thing for my dashcam, but for the rear camera I went up over the doors. Same end result, just more tucking and less trim removal.

I don't see those taps having a 3rd wire to provide power when the car is shut off, though? At least not for my car. I don't think these would work if you want to enable parking mode.