The plug for the tail lights on a 65 is on the cowl. I would actually unplug it, it kind of sounds to me that you may have a direct short in the tail light circuit since everything works until you hit the lights. Unplugging the harness would eliminate everything from the firewall back. If that does stop it then track it down on the harness to the back end. If it doesn't stop it then you have at least eliminated that whole harness as a possiblilty. Let us know what you come up with.
