I ended up taking the bumper loose on one side at a time which allowed me to remove the old backup lights and install the new ones without actually taking the bumper completely off. You pretty much need to loosen all the bumper main bolts but only take them out of one side at a time. And be careful not to let the bumper hit your painted surfaces. Also use a flat washer under the non carriage bolts on the bottom to prevent the tightening of the bolts from wrecking your chrome plating.
I made the mistake of removing the bolts behind the license plate. It turns out that you don’t need to remove or even loosen those because they are not attaching the bumper to the frame. I may be remembering that wrong, I hope not. Just leave them till last and only remove if necessary. I do remember they were a pain to deal with and I think I found that it was unnecessary.