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You have a vaccum leak somewhere. This is one of the most ccommon and most frustrating of corvette repairs. Do a search for corvette vaccum repairs there are some real helpful websites. Read a lot before you do anything it is helpful to know what controls what function. If you start messing with the vacum hoses like the previous owner of mine did it can be a nightmare.
This is a good one:http://vetteworks.tripod.com/techdocuments/Vaccum.html
I had this same problem with one of my headlights. Part of the actual headlight had come loose (all but one of the screws were missing) and was stuck on the body. If that's the case, you can probably pry it loose and put the screws back in.
It should be "locked" when in the up position, but you should be able to lower it with the engine off.
You can remove the bezel around the lights to easily see what's going on, but you should be able to reach from underneath and find two flat pieces of metal pinned together to make a "knee" joint between the two bulbs. In the open position, this joint is kind of like a hyper-extended knee joint that's locked into place. Nudge it in the opposite direction, and it will let the headlight close.
If that works, then the mechanical part(s) of the light is fine.
The most likely cause is a leaking actuator seal. There are lots of threads here and how-to articles on-line that step you through a seal replacement.
There are other causes: problem along the vacuum line (cracked line, pin-hole in line, bad T connector, etc.). It could also be the headlight relay. Does your '72 have two headlight relays or one. If two, you could try swapping the vacuum line from the other relay and see if the headlight works. If so, you have a relay problem for that light. If both share one relay, then I think you're back to the actuator.
I'm sitting here looking out my shop window at "Old One Eye" as I write. Frustrating as you know what. Sometimes they work like a charm - sometimes like this morning, I can't beat one of them down.
Here is a good thread with good links for troubleshooting.
Good News! I started my vette this morning for a friend to hear the LT1 engine and the eye up light went down! I tried it several more times and it worked every time! I think that since the vette has been a garage queen and not driven that something may need oiled. I have an appointment tomorrow with the vette Doc to check everything out! Thanks for your responses!