I agree, use a relay. I got mine from Partsexpress for $2.
Link
You can connect to the reverse lights in several different places along the spare well wall near the tailgate side. See
this article for some pointers.
I made my reverse connections near where the tailgate wiring enters the grommet for the tailgate. That was the closest point to my relay and to the video module. I connected to yellow/white + and brown - reverse wiring. I have tons of pictures so if you need anything just let me know.