I'm new to the C-10 world, did not see any extra space on the bars for techmount bracket.
There's no extra space on the bars for
anything on a C10.
Looking at the Techmount website, I see a few possibilities, but I don't know what might or might not work. The mirror mounts would bolt on, as the C10 has standard 10mm mounts, but would probably hit the dashboard when you turned the front wheel. A stem mount might work if you drilled a hole in the ignition switch cover to allow access to the steering head stem, but would be in the way of your keys.