A blinking light? That's a new one, I've never had that happen before. One of my other cars (not a GP) will sometimes have the light come on when I start it. But when I get home, I shut it off and get the test tools and start it again and it's fine.
If the light is blinking I can think of a couple scenarios:
1. Loose wires at the battery. Does it happen when accelerating/decelerating?
2. One of the cells in the battery is toast, and voltage dropped enough that the ECU is affected (hence the car shaking).
3. Alternator is not charging properly or only part of the time and the battery has finally discharged enough to start affecting the electronics. I've had a regulator work at idle but when revving voltage would drop, make sure you check idle voltage and also when revving up to 2000 RPM or so.
4. Some other loose wiring somewhere, you don't want this one cause it'll be a real pain in the arse to find.
