The headlamp doors are vacuum operated and open when vacuum is removed. There is a
leak somewhere in the system. You have a vacuum supply from the engine, a check valve,
a vacuum chamber, a valve on the headlamp switch, and an actuator on each headlamp
door. Visually inspect all of the rubber vacuum hoses for breaks or cracks, listen for
leaks (hissing) near the actuators, switch, reservoir, and all connections. Make sure
the check valve only passes air one way. At this age it could be any of the above, but
back when this car was newer the headlamp switch and the check valve were common
failure items.
 There may also be a manual valve under the hood, I don't remember if this vintage
Tbird had one.
 If there is a leak, the engime will likely idle rough. If the check valve is
defective, the engine will idle normally but the doors will open as soon as the engine
is turned off.

Do they open when lights turned on?  Thats pretty important to help solve
it.

If they open with lights on, engine running it's likely a leak.

Work your way back from the door (the headlight assy) actuator.

One or both of actuators, tubing to it, the control valve, may be leaking
vacuum, or the control valve itself bad.