You have 3 fuses on the brake lamps 1 for the brake lamp switch 1 for the third brake lamp(chmsl) and 1 for the brake lights. The under hood stop lamp fuse and the under dash chmsl fuses must be ok since the chmsl is working there is another vehicle stop fuse in the L. side dash fuse panel it can be bad or you have a wiring problem. If you have a test light you can check for voltage at the Lt blue wire at the rear junction block at the rear of the frame on the drivers side. remember Gm used the same color wire for both turn signals and brake lamps. I have attached several wiring diagrams to assist you the brake lamp circuit in question is high lighted in yellow.
ASE Certified Master Technician
30 years multi line tech ASE cert master tech ASE engine machinist, 9 years GM dealer exp.