sounds like a vac line.
I did a search here a few months ago for AC problems in the later C4 vettes.
Lots of info.
One or 2 posts with pics that even show ya which lines under the driver's dash to check.
(of course, been waiting on the weather to find time to check mine)
My AC was simply not responding until I had driven several miles.
After replacing a few split and dry rotting vac lines up around the fuel rails, I now have instant control again.
BUT,
it all comes out on the floor and a bit on the windshield.
nothing from the main vents.
So thats the next hunt.
Good luck
Rain