Hopefully, you'll be able to discover a few pieces of evidence your car had the GT options added at the assembly plant. Such a rare sought after option, and we see many more GTs on the road today than were actually produced. Your car was a NJ plant car. That could give you at least two advantages of finding evidence your car was or was not built as a GT. The buck tag was already mentioned. We have read several examples of owners of early cars from this plant discovering a build sheet taped to the wiring harness behind the dash bezel. I've got two 66 cars from the NJ with projected build dates of 3/23/66 (unrestored Conv) and 4/15/66 (GT coupe) that I have found build sheets for both cars. If you find the build sheet, you can look for a "5" to appear in the section of the build sheet for moldings/decor group/tailgate. If you are lucky enough to find the build sheet, the paper will be a bit fragile. You'll need to use car removing it from the harness and trying to unfold it without destroying it.
If the quarter panels have not been replaced, You can also remove your rear interior panels and inspect the area of the quarter panel where the quarter panel emblem would have gone. Should be smooth without any holes welded up where an emblem would have gone. Cars built as a GT from the assembly line, would not have rocker moldings.
If your fenders are original to the car, you can inspect the lower inside sections nearest the front wheel for any welds where the rocker molding would have been bolted. Should be smooth.
There will be two harnesses for fog lights: a small harness that runs from your fog light switch to a few inches through the firewall to the engine compartment, and also a fog light feed that is a single strand grey wire that connects from your fog underdash harness to both fog lights. An original fog light feed will have two short ground wires taped to it with black plastic electrical tape. Look for an original tag with engineering number near the end connecting to the fog underdash harness.
As previously mentioned, you can inspect your two fog light brackets attached to your grill. In addition to ?Top? stamped in them, you should also see LH and RH stamped next to it to designate left and right.
-Matt