Backup lights, wipers, switch

67 Barracuda- trying to solve a wiper problem that is affecting the reverse lights.

67s came with the variable speed motor (2822962) and switch (2770378).

Mine has a variable speed wiper motor, and the switch was apparently replaced with a 2 speed wiper switch (2820525).
The 2 speed switch has the same number of connections as the variable switch, except the green and red wire connector on the switch is mounted 180 degrees- those 2 tabs are the opposite way.

From the switch are:
DK Green - to motor
Red - to motor
DK Blue - to motor
Brown - to motor
Brown TR - to washer
White - to backup light switch, yes, on the tranny, it then goes to the backup lights

The wiring at the bulkhead to the motor is short 1 wire:
Empty (s/b DK Green)
Red - to motor cylinder
DK Blue - to motor, the top
Brown - spliced, one wire sent to the cylinder, one to the top of the motor

The wipers work and there are 2 speeds.
When I put the car in reverse, the backup lights will not light. If I turn the wipers on with the car in reverse, the wipers do not work. If I play around with the wiper switch, and usually it is making a clicking sound, the wipers come on and the reverse lights.

I replaced the dash harness and the engine harness with new. I've grounded everything, and made sure the switch is grounded. I have checked the wiring diagrams.

Any ideas on whether the 2 speed switch could damage the motor?
Or if the wiring to the motor is ok for making a 2 speed switch work a variable motor, which was probably their goal?
If I replace the switch with a variable switch, where does the DK Green wire go to exactly?
And, finally, is there a better solution to the factory idea of getting power for the reverse lights through the wiper switch?

Any help is appreciated. I know this is long, but I have done my research, and searched the forums- just could not find anything on my exact situation.