David, Lack of continuity does not necessarily mean that the wire itself is broken. Not all crimp wire fittings are created equal and neither are the installers. I have found crimp fittings where the conductor was not touching the fitting but crimped around the insulation.
My first inclination would be to disconnect both ends of the wire and replace the fittings or if you have really good probes for your DMM(I'm assuming that is what you are using for trouble shooting), pierce the insulation with the probe tip on each end of the wire and see if you pick up continuity.
Peterson soft mount Clearance lights are notorious for the crimp fitting not touching the brass fitting inside the light.
If the wire is bad, it may be possible to tap off any other 12vdc source in the slide. My cabin/LR slide has more than one source wire from the stationary wall to the slide.
I agree with ScottG, don't try and remove the paneling glued to the slide, that is a lot of work and ultimately very expensive.
You signature says you're in Glendale is that AZ, CA or ?. If it is CA, PM me and maybe we can get together to see what can be done, I'm less than 5 miles from Glendale, CA.