Gauges and rough engine when Ambient temp below 40 from cold start
I more than enough experience with electrical but not with Corvettes. This is the very first thing I would do even if it doesn't solve your problem.
Get a good multimeter and set it to resistance.
1. Check the negative battery terminal, that means check the post with a multimeter lead and check the terminal. You should get no more than .02 Ohms resistance. If it is higher .02 remove the negative terminal, clean reinstall and check again.
2. Repeat this everywhere there is a negative grounding terminal like engine to body, the negative side of the battery to the body, the grounding terminal that is close to the rear differential, everything.
3. After you check all negative terminals you can then check wires, especially those you suspect. End to end, terminal to terminal, though connections and at connections. A safe rule on short wire is .04 Ohms rom end to end. Longer wire allow for more Ohms.
4. Troubleshoot the temp sending unit.











