Mix dry ingredients and rub onto clean brisket. Wrap brisket in heavy-duty aluminum foil. Set grids at highest level and remove warming rack.
Set grill to low heat. Add mesquite wood chips in a smoker box or on top of the flavor screen. Slow roast for up to 8 hours at 200°F. Add wood chips as needed. After 3 hours, check for doneness every hour using a meat thermometer. When the meat reaches 160°F (or 170°F for well done), place in oven at 180°F for two more hours until ready to slice and serve. Serve with beans, slaw and cornbread for a real Texas experience.