Orange77, congrats on your purchase and welcome to the site. The problems you have listed are fairly common to these cars and also a bit chronic I might add. The first question I have to ask is are you going to be fixing this car yourself ?? If so you've come to the right place and we can talk you through most things. Most people on this sight have either experienced the problem or know someone that has. A search of our previous posts is also a good idea.
If your not going to be doing the fixing, look for someone with C3 experience in your area. Don't just take it to your average tune-up/repair shop. Check around in your local area for any Corvette Clubs, or check to see if you have an NCRS (National Corvette Restorers Society) Chapter near by to get some recommendations from experienced owners.
Your headlight problem sounds like a vacuum leak. That same leak is also possibly affecting your heater/temp controls if they do not function properly. Vacuum leaks are a bit of a pain, but they can be found using a vacuum pump with a gauge and isolating each of the connections at the different components. If the vacuum hoses appear to be the original, many people choose to purchase a new vacuum hose kit and replace them all. Unless the're in really bad shape, I prefer to cut off about 1/2" off the end of the hose at the suspect connection to eliminate the already expanded section and provide a tighter fit, just make sure you have enough slack in the hose to cut off a small section. Look for a vacuum hose diagram for your year, there are a lot of connections to be checked.
The rest sounds like electrical gremlins that could be a combination of several things. The tach could be anything from the tach connection at the distributor to the small circuit board that's on the back of the tach. Look for a reply from Adam's Apple, he should be able to help with the tach based on what if does, if anything, when to turn the key. As Jeffm posted, the gauge lights could be the flexible circuit connector on the back of the gauge cluster.
One give away to many electrical problems is work done by the previous owner(s). New stereo installations can spell trouble if somebody went a little crazy with the wire cutters and blue splice connectors. Check out the electrical section of our site, you should find a link to a wiring diagram for your year.
Hope this helps you to get a start, check a few things out and get back to us. Good luck !!
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John Sigmund
valkman57@sbcglobal.net
NCRS Member 61302
NW NCRS Chapter Member
Duct tape is the new Black !!
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