I know the socket grounds the bulb. There is a ground wire from the socket that goes into the harness. The harness goes into the body somewhere. That ground wire has to attach to the body or the chassis somewhere. Where is that connection?
I did remove the bulbs and the other lights no longer come on, so it makes me think it is a tail light ground issue. On the alternator light issue, I found that once I disconnect the battery the light goes off and does not come back on when the battery is reconnected.

 

"The socket is the ground"? Isn't the socket plastic? It has to be grounded from the socket shell to a point on the pan somewhere doesn't it?

 

Absolutely. I can't find that "somewhere". This is my first Camaro. Someone has to know where the grounding point is.

 

Stick your head in the trunk, then touch your chin to your chest...now you're looking at the rear of the trunk area. Look at the braces where the trunk meets the tail panel. I believe that's where mine are, I can confirm when I get home.

 

If pulling the bulbs out fixxed the problem then put new bulbs in, 1 of the bulbs is bad. Sometimes the brake or taillight filament in the bulb will break off and touch the other filament and energize other circuit, happens alot with 1157 bulbs

 

It's there and it is hooked up. I took it off and cleaned the connections. Still; have the same problem. i also made a ground from the block to the firewall. Still have the same problem.

 

I found the problem! Someone had a 1156 light bulb in one of the sockets. It was grounding the brake light to the running light and lighting up the whole running light system. Now to tackle the alternator. Thanks to all who helped.

 

Have you tried disconnecting power to the alternator yet to see if the battery still craps out?

 

Disconnecting the alternator stopped the battery drain. I guess just cause its new doesn't mean it's right.