Only the purple wire from the NSS feeds the rear backup lights (why they used purple). The other white wire is the incoming +12 V supply lead. Doesn't matter which outer terminal is which on the NSS, but best to try to keep it like the factory did.
What is confusing is why the wiper switch is involved. Like I said, the designers often used the wiper switch as a convenient terminal tap. If you look at the wiper switch, I think you will see the two "B" terminals are directly connected, ("B" = "Battery", but not exactly). That means the white wire is always connected to the incoming pink wire (wiper switch uses also), which connects to the black "accessory bus" from the ACC terminal on the key switch. That terminal gets power in "ACC", "RUN", and "START" key positions, as I recall.