Flickering lights!?!???

Here's what's happenin on my 83zxt. At idle with no loads I have no problems but the minute I turn on the headlights, or parking lights plus blinkers, or parking lights plus apply brakes, or take the car above 4K rpms every stupid light in the dash lights up. Even when I turn on the radio (this is with no other loads) and the antenna goes up the battery light flickers; while the atenna is going up or down. I put my trusty meter on the battery to check voltage and everything seems normal. The voltage never drops below 14 and never gets much higher than 16 (15.6 was the high I believe), this is through out the rpm range

Now the alternator is brand new, I installed it and went for a drive, everything was fine untill I jumped on the throttle (gotta love the speed). At that moment all lights in the dash went on. The battery is also brand new, bought her about a week ago. and is the biggest I could find.

I should probably mention that I do have a crappy aftermarket cd player but did not have it powered on when these problems first started. So I know thats not my problem.

Could this be fuseable links? If so which ones and where are they located?

Thanks,
Josh 83zxt