I have a '68 Rally Red Roadster that was repainted in 1999 76XXX original miles. Like your subject line I have one bump in the paint about the size of a quarter. I had head the cause before but all the guys chimming in on your entry just confirms it. I was also at a get together last week and there were also 2 other '68s there and you could see the rivets to varying degrees.
It's a shame because the car has been garage kept and only has 9,000 miles on it since it was painted 13 yrs ago and is shiny and deep.
My painter friend said essentially that same as one person commented. Drill them out, clean the area of all contamination seal holes with top line adhesive, remember we have adhesives now that weren't even thought of back them, and then do the body work and paint. The only other option is to buy a door to door new front end ($2,000-$4,500 depending on vendor) and repaint.
I bought the car 3 months ago with the flaw, because of the condition of the rest of the car. I made a Car Show Storyboard calling it a Survivor and will live with it through 2014. After keeping it stock for a year then next year I'll have it fixed and repainted Corvette Torch Red. I've had 2-1998s, 2010, and a 2012 Grand Sport all Torch Red and I'm addicted to that color.
Like one person said "GM didn't intent for them to be around as long as they have". Just sold my Grand Sport to make room for the new '68 as my wife has me on a 2 corvette diet. The GS had all the bells and whistles, but honestly I'm enjoying having something that I can get under the hood with a screwdriver or actually change things.
I get just as many thumbs up, wave and smiles with the '68. I'll just enjoy it for the 45 yr old sports car that it is...................hope you do to.
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God Bless, rick
'75 Steel Blue Stingray Coupe
'75 Hot Red L82 Stingray Convertible