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Could also be one of the vacuum motors. Mine is at the shop having them all changed, and the hoses all replaced while they have the dash out. I've turned into a geezer - did this kind of stuff myself on the Shelby I had for many years. But between arthritis and being a fat old man and the tight quarters in the C3, George at the shop is my new best friend
One of the vacuum motors is in the air intake - a real bear to get to. Another is under the right kick panel - simpler. Two are on the air box behind the gauges. I just figured do 'em all and be good for another 47 years...
Dewitt, with the car running, check for the sound of a vacuum leak in the vicinity of the Heater & A/C Control Assembly on the center console. photo courtesy Paragon Corvette Reproductions https://www.paragoncorvette.com/p-36...-assembly.aspx
The Heater Control Switch has a plastic Pivot that holds it together and if that pin breaks (mine did in about 24 months when new) you will get a vacuum leak and the controls will not respond to input. photo courtesy Paragon Corvette Reproductions https://www.paragoncorvette.com/p-35...ol-switch.aspx
If that is the case, just access it through the passenger side of the console by removing the cardboard trim panel and replace the pin, or the Heater Control Switch and you should be back in business.
Good luck, and let us know what you discover... GUSTO