[SharkPilot]

Years ago I had a strange problem with my '69. At idle the engine would stumble a little just as the headlights and dash lights flickered. This only happened at night and at idle speed and was very intermittant. What I eventually found was some corrosion under a TIGHT ground connection at the battery. This was a side terminal battery behind the seat as all Sharks are.
Once I cleaned the contacts and reattached the cable all was well.
What I deduced from the experience was, the alternator handled all of the electrical loads just fine at higher RPM but once the engine got back to idle speed the alternator couldn't keep up with the demand if the negative cable lost its connection. Once that happened the engine would stumble and lights would flicker. The car never had a start up problem. The engine would crank and start just fine every time.
That car had no electronics or fuel injection at the time so it was much simpler. I would speculate that any interruption in the voltage with our electronicly controlled cars would cause a bit more havoc. Your lights flickering and the dash going crazy are good clues. Perhaps the voltage problem affected the VATS like others have suggested and disabled the car for 10 minutes.
Since your problem happened at or near idle, with the alternator turning its slowest, I would go after a battery connection.
Your low voltage at idle with the turn signals on also suggests a battery connection.

I hope all of this helps a bit and I'll be watching this thread to see what you find.
All the best, SharkPilot