According to the 95 FSM, the manual back up light switch uses the same wires as the back up light portion of the NSS, so if you have broken into that harness and run that circuit through the new switch, I'd expect either a problem with the switch or the fuse rather than with your wiring job.
Power comes from fuse 11 in the PDC, via a dark blue and white wire, through the switch, to the backup light line, which is brown/light green.
If there is a harness problem that goes very deep, though, you might do better just to find another source of 12 volts and run it through your switch.
I say this because the wiring diagram is not always entirely informative, and my experience with the harness on my 95 was that wires often go in one end and seem not to come out the other, and you can spend days trying to troubleshoot when it's a matter of minutes to say, **** it, let's roll our own.