Can't find my C3 stuff, and several things can go wrong, but the most common one is for the gear that is driven by the distributor (and turns the tach cable) to have its teeth stripped.
The tach drive/cable is at a bad angle. IIRC, the gear is under a screw-on cover on the distributor housing that the cable goes into, and the cable goes into it.
In any case, it's cheap and easy to replace, and somebody used to make a trick drive to keep it from failing. Don't remember how it worked.
Hopefully, the gear on the distributor shaft is ok. While you can use a drill to check the tach, the only way to check the gears themselves is by inspecting them.
Besides searching, you might also look at some of the large Corvette supply house catalogs for replacement units to get an idea of what it's like. Occasionally, they also have installation instructions or breakdown sheets.
It might be worth picking up a basic C3 manual; they're great cars, but they do sometimes need attention.
