We can break it down into logical steps. Hopefully, Junkie will keep me straight here...
http://www.corvette-101.com/images/vacsys.jpg
Red closes the lights, and is the normally open side of the relay.
Green opens the lights, and is the normally closed side of the relay.
Yellow is the common source vacuum from the tank.
The relay is a normally closed (green side) vacuum switch. Vacuum applied to the metal control line changes vacuum direction to the normally open (red) side.
The line in the center with the tee is the up/down control line. Vacuum present here closes the headlights (your headlights will go down when you start the engine if they are up). Vacuum absent here opens the lights (assuming vacuum is present at the source).
Troubleshooting:
Check for correct routing of the hoses.
Pull both yellow hoses. Plug one of them. Start the engine and check for 10-15" vacuum at the other yellow hose. You can check at the vacuum tank. If you don't have any vacuum or have low vacuum check for leaks in the hoses or in the vacuum tank, or a bad check valve (gray metal, 3 connects) or a plugged vacuum filter (white plastic, 2 connects).
If vacuum is good at the yellow, jumper the yellow hose to the green hose with a smaller piece of hose or a small piece of tubing (or use a hand vacuum pump if you have one). If the headlight goes up without effort then the actuator is ok and the vacuum relay is leaking out the vacuum. If the headlight doesn't go up or goes up with difficulty then the clevis rod seal is shot or the hose is leaking (bad). You've already said the lights go down OK, so the diaphram must be good.
One side being bad will likely affect the other side operation too. Check the other side when done.
http://www.corvette-101.com/vacuum.htm