GM used two different 'strategies' on Corvettes.
1953 to 1972 used a coolant system where an airspace was required to allow for expansion as the engine heated up. Most copper/brass radiator cars had an expansion cavity inside the radiator (69's were different) and you simply filled up the radiator through the cap opening to a certain level, leaving a few inches head room. There was no external expansion (surge) tank or overflow tank.
Most cars with aluminum radiators had no internal expansion tank or filler cap on the radiaitor. They relied instead upon an external remote expansion tank (surge tank) which had the filler cap. This tank is also to be filled only partially to prevent the famous coolant puke after shutdown.
1973 and newer Corvettes all had a copper/brass radiator with an intergral filler cap, but had no internal or external expansion tanks. The radiator was intended to filled to the brim. To allow for expansion, an overflow tank (usually plastic) was connected to the radiator filler neck with a small tube. As the coolant expanded, the excess would flow to the overflow tank for storage. Upon engine cool down, the excess would be 'sucked' back into the radiator keeping it 100% full at all times.
It sounds like someone has installed a pre-73 radiator on your car but did not complete the retrofit by adding an expansion tank. Your choices are to add a tank now, or upgrade the system to post-73 specs.
