Interesting. I had a Grand Prix back in the 80's. One morning on the way to work, I hear clicking coming from the rear defroster switch, or so it seemed. I just turned it off, and went on my merry way. After work my car wouldn't start. No engine turning, no nothing. It turned out to be my "-" battery cable was loose. So my problem was a weak, or intermittant ground. That probably applies here too. The clicking is some kind of arching going on. If it were a wire against the ground(body), I wouldn't think there would be a pattern to it as far as clicking goes. Are you sure the sound isn't from the light switch panel? Does it happen regardless if the lights are on or off? The fact that the lights dim, and ampmeter takes a dive, means excessive current is going somewhere. As a last resort, you can remove one fuse at a time, start the car, and see if the problem goes away. That would at least narrow the problem to a specific circuit. Keep us updated.
Mike
