Soak mesquite wood chips in water for at least 30 minutes.
Preheat smoker to 225 - 250 degrees. Sprinkle soaked wood chips over coals.
In a small bowl, combine brown sugar, salt, paprika, mustard, garlic powder, onion powder, and red pepper. Spread mixture over all sides of roast. Let stand at room temperature for 30 minutes.
Place roast in smoker. Cook, covered with smoker lid, until meat is very tender, 11-12 hours. Remove from smoker, and let stand for 30 minutes. Shred roast, discarding fat and bone. Serve with Carolina Vinegar Sauce or your favorite barbecue sauce.
Carolina Vinegar Sauce.
In a medium bowl, combine vinegar, brown sugar, red pepper, salt, black pepper, hot sauce, and smoked paprika. Cover, and refrigerate for up to five days.