Something you might want to check is the ground point at the rear of the car on the driver's side behind the rear wheel fender liner. This is the ground point for the Fuel Pump Control Module (FPCM). I've found posts regarding problems with this ground point. Separate it and clean it, remove any corrosion you find, and re-assemble. I've also read that this is a sore point on the C5/C6 corvettes as well. So it's worth checking. A bad ground can result in intermittent electrical problems like the one you describe.