Wipers & 4 Speed Reverse Lights

Why the heck are the reverse lights and the wiper switch conjoined twins?
When the reverse lights don't work, the wipers do not work. With the car in reverse, if I turn the wipers on and off until they work the reverse lights come on, or if I mess with the shifter the wipers come on. If the wipers go off, the lights go off, and vise-versa.
The wiper switch clicks as the wipers and lights try to come on.

New wiper and reverse switch, I grounded the rear lights, new wiring, new, new, new. Saved the old stuff and tried that again. I followed the wiring diagram, and everything is wired correctly.

Do those smarter than me change the wiring?