Check for 12 volts at the fuse. A good fuse means nothing if no voltage is present. Fuse #13 (20A) in the Power Distribution Center powers up the brake lamps switch. Equally important is checking the lamps ground circuits. All else checking out ok, replace the brake lamps switch.
In the front drivers side under the cab you will find where the electrical harness comes out of the cab. There on the cab side should be a light blue wire which is the brake signal to the trailer. Make sure on the plug that attaches to it there is a light blue wire going to the back of the truck. This wire was omitted on my truck! Bought a brake system for mine even though it came with a towing package it didn't get the blue wire! I had to splice into the wire and run a wire to the back. Hope it helps