Along the firewall wiring between the booster and coild is where the plugs for the transmission switches are.
Did you check to see if the wires are intact where they go into the transmission? Most issues I've seen with them is the fact the wire breaks right where it goes into the epoxy on the metal body where it threads in. You can't repair them. They have to be replaced.
If you have issues with burning them out due to brighter reverse lights, then you need to install a relay inline for the lights.