Fuel Feed Problem
The C3 Vette uses a fuel pump that feeds the carb and pumps the extra fuel back to the fuel tank, recirculating it to keep it cool.
Fuel can "drain down" between the carb and the fuel pump if there are loose connections or old ratty fuel hoses that allow fuel to permiate the hose. If this happened, however, you would smell gas fumes. Check your hoses and conections starting at the carberator and moving rearward.
Change your fuel filter which is probably located between the carb and fuel pump. On Q-Jets there is also a filter inside the carb body where the fuel line connects.
Test your fuel pump to see if you are getting sufficient flow. Ab easy way to do this is to remove the feeder hose from your carb intake and have someone crank the engine over while you hold the hose in a container. You should get plenty of gas coming through in the first 2-3 seconds. If not, then the suspects become: 1. Fuel pump 2. Plugged pick-up in fuel tank. If it were me, I would tackle the fuel pump first.
Note: Last year when I disassembled the engine block on my 78 Vette with 90,000+ miles on it, I removed the fuel pump for inspection. Guess what? The actuator arms inside the fuel pump that is actuated by a push rod ring on the camshaft was almost impossible to move up and down. That meant that the fuel pump was almost froozen solid and was not pumping the volume and pressure of fuel needed by the engine. Seriously, I have no idea how the engine ran with the fuel pump being that bad.
Remove the fuel pump that is held on with 2 bolts and check its operation. When in doubt, replace it as they are relatively inexpensive.
If the fuel pump is fine, you may have a restriction in the fuel line of at the pick up point inside the fuel tank.
And one final possibility is ... make sure that you do not have a vacuum in your tank or fuel line. This can happen when the gas cap or the charcoal cannister do not allow air into the system. If this happens, the more the fuel pump draws fuel from the tank, the more vacuum builds within the system. This would explain why your engine is hard to start after sitting for awhile. If vacuum built up while you ran the car, then vacuum in the tank could "suck" the fuel out of the fuel lines as it attempts to equalize internal pressure in the tank.
Try these ideas out and let me know what happens.