This is a great idea but i would personally run all new wire through split tubing. I would probably add a switch because you might not want that reverse light on all the time when backing up. Just a through i know its within the law in PA to do exactly what you are doing. Love the idea tho.
I was looking for it when installing my back up camera(couldn't find it ). I just ended up splicing into the revere lights directly.Someone correct me if I am wrong, but there is no wire for the back up lights in the 7 pin plug on the truck.
Also, first step is to see the amps that light draws before making any wiring or relay decisions.