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Just picked up a 91 6sp not too long ago. I'm having an issue at idle. If i'm sitting in neutral at a light and my turn signal is on, every time the turn signal lights up (flashes) my voltage drops a bit and so do the revs.
What is your system charging voltage? Should be 14.5 volts. Have your battery tested. A weak battery causes unusual happenings. My guess is a bad battery.
Sounds like a bad Display; either a cracked board or weak solder joint on the Board. Doubt your actual RPMS are dropping which you could confirm with a Scanner. Turn signal function is simply zapping the Board, probably at the Indicator input which causes a voltage drop at the Power Supply and your Tach display goes down with it (I'll presume the backlighting is too). You might make sure that the Connectors are good, but unless someone got in there and monkeyed with them or they were somehow exposed to excessive moisture, I'd say it's the Display and probably something you can live with.
There's also serial data to the Dash which, if something is intermittently taking it out, might cause a driveability issue. In fact, that's the only connection I can think of to the ECM in this circuit and the ECM is what controls idle. Most ECM's need at least 9.6 volts, though I've experienced a reduction in idle quality at anything below battery.
You need the schematic to troubleshoot, but turn signal circuits are fairly simple. Power to the light from a fused ignition source through the turn signal switch and then to the flasher which simply turns the power on and off with a couple of indicators spliced into the circuit for the Display arrows.
You might Google this as it's not so generic to the Vette that you need specific info to start figuring it out - or you could, since they're cheap enough, start by replacing the Flasher to see what happens. Also check wiring at the Lights as it is subject to corrosion and if one or two are dropping volts, that might be enough to drop system voltage, though the amperage for any single light is fairly low.