There may not be a back up wire under the dash... BACKUP light switches are in one of two locations on most vehicles.. I will give examples.
GM normally puts it on the steering column, but what if you have a stick shift with a "4 on the floor"? Ford put that one on the side of the transmission.
Now there was (on my AMC with Ford Transmission) a wire under the dash in a bundle on the far left but it was buried.. all the wires to the rear were in that bundle. .. and there was a connector. Right where teh salt water spray hit it in the winter.. (Very bad design).