Mix together salt, pepper, garlic, chili powder, and cayenne. Rub brisket with spice mixture. Let sit a room temperature for 1 hour.
Prepare your grill using the kettle grill, bullet smoker, or gas grill method, (see links for instructions) using apple wood chunks or chips (see Fuel and Flavor). Place brisket, fat side up, on grill grate. Maintaining a temperature of 225°-250° (if using a kettle grill or bullet smoker, replenish fire with unlit coals, as needed, to maintain temperature; see instructions), cook until a thermometer inserted in meat reads 160°, about 6 hours.
Remove brisket from grill, place on two large stacked sheets of foil; fold up edges. Pour in juice; wrap foil packet to enclose brisket and return to grill grate. Cook until a thermometer inserted in the thickest portion reads 190°, about 2 hours.