The “T” in the vin number indicates that it was originally a six cylinder engine car. Does it still have a six cylinder engine in it? Six cylinder engine cars came with 4 lug nut wheels instead of the more common 5 lug nuts you see on most early generation Mustangs. It is a bolt on conversion to put the front end stuff and a 5 lug rear end in this car. Has that been done?
An item that carries some more dates is the tag on the steering box. The tag is on a bolt on the top of it and is usually under an inch of grease. If this car still has a six cylinder engine in it, it is really easy to see. If you have V8 engine and power brakes it is tougher. See if it has this tag and write down all the numbers.
My car has a vin number with the consecutive last six numbers as 123144. If was built on January 2nd. Your number of 105503 is even earlier. But there was a late fall strike and all sorts of cars languished on the assembly line or were pulled off not complete. One thing that is not commonly known in this happy is that most of the large sheet metal parts have date codes “stamped” on them. You front fenders should have dates on the flange that bolt's it to the engine compartment. They can be covered in several coats of paint. Usually they a two numbers and one letter. If you open the trunk and trace around in the rain trough that keeps the water out of the truck, you can usually find the rear quarter panel date codes. A great place to look is in the area behind the rear seat back. Remove that and the interior side panels and there are dates galore. And only one coat of primer.
These dates are usually older than the date your car was built. Of note this car should have the early “recessed” rear quarter panel reflectors based on its early vin number. This type of investigation is fun. You can almost trace the building of the car.
But again lack of production parts on the line can introduce wild swings in the date codes, so they are just more information to assist in the origin of you car. Current knowledge indicates that your car is too early to be a GT/CS. So is my vin number. Yet my car has all of the GT/CS original factory pieces on it. But its Marti report says it is not a GT/CS which is the current gold standard of authenticity.
It is my opinion that due to all the turmoil between Ford and the So Cal Ford dealers just prior to the debut of these cars, and the fact that cars were pulled from the line and pre-staged for conversion, that the cars at the debut may not be Marti verified. They had already been ordered as a normal Mustang Coupe, pulled from the line and converted. A GT/CS that was built on the San Jose line that will not be Marti verified.
The search continues to prove this. Someday we may find the definitive early GT/CS that will verify this theory.
Rob