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My '99 has been doing the same just recently. The fuel filter seems very unlikely, since the motor runs fine going through the gears (for me). I'm tending to think it's time to get around to cleaning the grounds, since I've also got some intermittent turn signal flash rates.
Then again, a google search of 'C5 corvette idle drops' returns more than a couple of suggestions, including this thread indicating a cleaning of the MAF and throttle body might be in order: https://www.corvetteforum.com/forums...en-idling.html
Think I'll give it a try this weekend.