The core support or radiator support, is attached to the inner fenders, along the bottom edge, as well as, to the frame-to-core support perches. There are also 4 bolts, that go through the lower front of the core support, that attach it to the mounting flanges of the inner fenders. There are also two bolts, in the nose of the front fenders, that secure them, to the radiator support. There are a total of 16-18 fasteners, securing the core support, to the inner fenders, front fenders and the frame perches.
As a minimum, I highly recommend acquiring this manual:
1960-1966 CHEV/GMC TRUCK FACTORY ASSEMBLY INSTRUCTION MANUAL