Continuing on............
Update: and bear with me... I'm no mechanic and relating all this secondhand...
The problem isn't popping up after they're turned off. When I turn the headlights off, they go down - and stay down - but make the staccato sound for several more seconds, then stop.
When I turn on my Parking Lights or Running Lights, the headlights flip up, but the lights themselves don't come on. They just flip up, which they've never done with the Running Lights turned on.
Initially, we looked at the headlight motor: passenger side is the one which keeps running for several seconds, as though a limit switch isn't being made or a signal isn't being sent. And the headlight control/turn signal switch as the source causing the lights to pop up when they are supposed to stay down.
Kevin and Sandy looked at several wiring diagrams and schematics, by the way, while troubleshooting the issue.
The first thing they did was replace the turn signal stalk/switch. The thinking was that let's stop the lights from flipping up unwanted before replacing the headlight motor so as not to strip the gears on the new one.
Problem is, that didn't stop the flip up when turning on the Running Lights.
They replaced the new turn signal switch with the old one and started back on the wiring diagrams. Finally, they came across a diagram that shows a headlight module located BENEATH the headlight.
On my way back to the shop yesterday, my turn signals wouldn't work. So we replaced the TS switch with the new one and they worked fine.
Sandy spent the day on his back under the dash up to his elbows in wiring, testing and following and tracing wires.
The issue, as I understand it, is there is no COMMONALITY between the two issues. No problem that would cause BOTH issues together, that is, the headlights flipping up when the RL are turned on and the delay in the headlight motor shutting off.
Kevin mentioned that it could be as simple as two wires touching due to insulation cracked/missing/eaten by a rat etc. - OR - it could be something like a problem in the dash cluster, the only common link that the two DO share. I also reminded Kevin that about 4 months after I bought this Vette, we discovered the notorious "battery leaked on the wiring harness" issue.
So I'm driving the car as is while Sandy does some research for the next couple of days. Kevin will be out of pocket for a week or two because of a trip to the Mayo Clinic to undergo testing himself (my buddy Kev has been on the list for a liver transplant for quite sometime now).
The only good thing is, these guys will NOT throw expensive parts at the problem, emptying my bank account while taking wild-a$$ guesses. They've always treated me well and taken good care of my Corvette AND me.
Any suggestions or insights you C5 guys can offer would be appreciated and passed on to my pit crew.
Jane Ann