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Try your 4 way flasher or turn signals. If they work fine, you will need to check the electrical schematic. I am not familiar with Corvette wiring, but worked on police cars for years. Usually with this problem, especially high mileage cars, the problem was in the turn signal switch and you could check it by wiggling the switch lever or moving the 4 way flasher switch. On all the ones I have seen, power goes through the brake light switch, and then through the turn signal switch and then to the bulbs. This is where I would start my search. Good luck!