We found High Intensity Bicycle Shop at the west side of town and luckily the shop was open and the owner/mechanic was there. The cable had broken close to the shifter itself and Tom wasn't sure he'd be able to pick out the short broken wires. While he worked, we walked down the street to get some lunch and wondered if this was the end of this tour.
Thankfully, Tom was able to replace the shifter cable and lubed both our bikes. Tom and his wife run their business mainly online selling parts and Kona bicycles, but they also have a snow bike they designed themselves. I got to try it out. Single-speed with fat 4"-wide knobby tires.