On a whim I checked to see if etrailer.com offers a trailer hitch for a 1995 Corvette (a random year for an older Corvette). They do.
etrailer.com/hitch-1995_Chevrolet_CorvetteTrailer Hitch Size:
1-1/4 Inch Hitch Opening
Towing Capacity:
200 Pound Tongue Weight
2000 Pound Towing
Trailer Wiring:
1995 Chevrolet Corvette Trailer Wiring
Code: C11705
Retail:$444.97
Price:$254.95
Features:
Perfect for light-duty towing, this custom, vehicle trailer hitch receiver features fully welded, gloss powder coated steel construction. Drawbar sold separately.
Installation Notes:
Drilling required for installation
Trailer Hitches for Chevrolet
Hitches are custom designed by Draw-Tite, Reese, Hidden Hitch, Curt, and Torklift to fit your Chevrolet. Choose the hitch that is right for your towing needs and your budget. All hitches come with a limited lifetime warranty and are manufactured in the USA. We offer over a custom hitch for virtually every Chevrolet on the road.
etrailer has a trailer hitch available for a 2013 Corvette too. Did not search for any years between 1995 and 2013. I was unable to find them for Corvettes newer than 2013. It seems that a trailer hitch may, or may not, be available for a Corvette depending on its model year.