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On the switch there is a little spring loaded button. Pull the headlight switch fully on and then depress the button and the shaft and **** will come out. Then you can undo the bezel nut to remove the switch.
In a way, I'm jealous; the headlight ****/shaft on my '79 actually comes right out of the dash. I suppose the aforementioned button/spring mechanism is broken and I've gotta tear the dash apart to replace them. Not looking forward to that part of the project.
All GM shaft-style headlight switches work that way.
Chilli, I think you're going to find that you need to replace the whole headlight switch to fix that problem. Make sure it has the vacuum switch - some of the parts store listings I've seen are for generic switches that won't work on a Corvette (unless you ditch the vacuum headlights).
In a way, I'm jealous; the headlight ****/shaft on my '79 actually comes right out of the dash. I suppose the aforementioned button/spring mechanism is broken and I've gotta tear the dash apart to replace them. Not looking forward to that part of the project.
I have replaced the headlight switch in a 73 with a/c without removing the dash. Cut the you-know-what out of my hand but didn't have to take anything off but one small section of a/c duct. If you have the switch to look at you can see the orientation of the plug and then start taking the old one out, using just feel. If you have large hands don't try it or, better yet, get your wife or gf to do it.
Gary