Hi. I don't completely understand what the problem is? There are different kits out there, but I will take a guess. There are spacers that go between the LED unit and the socket. Without them, the LED will not fit and press up against the back of the taillight housing.
I've been texting with Hugh and from what I can gather he is missing the harness that goes back to the lights. I'm not sure where the tail light harness is routed on a 66 but one of my suggestions is to get the factory harness and then adapt the LED assembly to that.