Then the other wire should go to your backup lights, right.
(as if you connected those two wires together your backup lights come on?)
All you have to do then is find the two terminals on the switch that have continuity only in reverse and connect your two wires to those two. (orientation doesn't matter)
Keep in mind that the switch may not be in the right position from the dealer, and may have to be adjusted. (might be why they are on all the time when you tried it before.)