Remember that the trailer light circuits are fused separately from the truck body light circuits, but they share some functions with/through the flasher. I'm not saying it's a fuse issue because the turn signals work, and those are the roughly the same as the brake lights.
Are the body turn signal light bulbs different from the brake light bulbs? They are on my '04, but I'm not sure on your '05.
On my body the turn signals and emergency flashers are amber, but the flasher needs to combine the trailer brake light function since the trailer uses the same bulb filament for both turn signals / emergency flashers and the brake lights. It's a trailer light converter of sorts for TV systems that have separate turn signals and brake lights. The flasher works like this 3-to-2 converter:
Tail light converter