Don't worry about the relay, that is a red herring. That is for the trailer tow light wiring only. The poster that said it fixed his problem must have his truck lights being powered by the tow harness wiring back in the rear.
Also, don't mess with the hazard switch and it's wiring. That is a separate feed. You need power on the brake pedal switch. It's not going to work until you get power down there. I have had the wiring break going to the pedal switch. The wiring and the switch moves each time you use the brake pedal, and it can break in two over time. The fuse must be good since it's used by the hazard circuit also.