[83GMCK2500]

1) You're in the wrong forum section, the 99 Tahoe is a GMT-400 platform which is the 88-98 section.

2) Here is a picture of the multifunction switch assembly. The portion of your harness that has failed is likely one of those wires and the harness is not separate from the switch. Quickest/cheapest repair is to solder the wires back together. Alternatively the Dorman replacement multifunction switch assembly s ~$52 from Amazon.com. I don't know what the quality of their electrical components are, some people don't mind them, I personally use Delco parts. Could also lookup vehicle on rockauto, search for the multifunction switch and look at their offerings.