I suspect what you are reading as C7 is actually CZ. That would conform to a '54 model. The C designates the Oakland, CA assembly plant.
I also suspect the tag reads:
GMC TRUCK & COACH DIVISION
GENERAL MOTORS CORPORATION
PONTIAC, MICHIGAN, U.S.A.That does not indicated assembly in Pontiac. If assembled in Pontiac it would have a P where the C is. Some were also assembled in St Louis, having an S code on the data plate.
The VIN busters are made for Chevrolets. GMC numbers will not work in them. Info on GMC numbers can be found at
www.oldgmctrucks.com