My f-150 came with a plug to cap the camera connector if I ever removed the tailgate. For this instance, I'd investigate t-ing off of that plug for both cameras. Then only the signal wire needs to be put on an A/B switch. Effectively, both cameras would be powered when in reverse, but you are only using the selected video feed.
2012 Ford F-150 Eco, Max/Max
Jayco 26.5 RLS, Reese Sidewinder