I have a 67 Pontaic GTO that experiences a flickering and dimming of the headlights and interior lights when the brakes are applied. When accelerating, the lights return to normal brightness. Is this an alternator problem, grounding problem??Is there anyone who has experienced this and knows what needs to be done to correct this?  

could be a low output on the alternator. My friend with a GTX had the same problem. I told him  to put a ground wire from his voltage regulator to a good ground. His voltage regulator was mounted to the painted firewall using a star washer that didn't scuff the paint enough. This solved his problem. Most people don't understand that electricity flows from negative to positive(electron flow). This is why it is so very important to have many grounds on a vehicle. You should ground the battery to the engine block, to the chassis and to the body of your GTO. A good ground is more important than a good positive. Another solution is to run a relay for your lights. use the power wire that powers your lights to trigger the relay. the other goes terminals go to the battery to the headlights through the relay. you would need two relays. one for the low the other for the high beams. most old cars don't get 12v to the headlights because of the resistance in the factory wiring. This will make your headlights brighter and still use the factory on/off switch for the headlights. Hope this helped.  

Sounds like you are are the right track. Check ground straps and have the alternator and battery load checked. You might also consider checking the regulator. Sounds like the requlator isn't pulling in when the added load of the 6 tails come on. That is a pretty good load to add to a marginal regulator. What does it do when you push the lighter in???? that is a good sized load also you might try that and see what happens. What does it do when the engine isn't running??? Turn the head lights on hit the brights and brake and push the lighter in and turn the heater fan on high then turn the wipers on, in other words max out the system. You may just have a bad connection at the battery or one that weak. Aren't electrical gremlins fun!!!!