I have a 95 vette that every so often all the dash lights start blinking and headlights start diming/blinking as well.
... One simple check is the ground connections at the battery ( NOT just the ground cable, BUT underneath there is another smaller lead that grounds to the frame . ) ........
I had a similar experience with my '89. It turned out to be a bad alternator. They are relatively inexpensive and easy to install (at least on the '89). Your ZR1 uses a different alternator but I believe it is installed in the same place on the engine.
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