Searched the forums and haven't found a fix on this yet. The red BRAKE light that lights up when you engage the E-brake randomly lit up and is always on when I turn the truck on. I have tried setting and releasing the brake, and turning the truck on and off. Most problems I have found in search are usually accompanied by brake issues. I noticed this happened after running through some flooded streets getting home from work, and if I hit a bump the light may turn off for a bit or flicker.
Either the E - Brake is not fully disengaged, or you have an electrical issue (short or faulty part). I would start by looking at the brake switch and work my way back to the mechanical portions of the system.