Heat oil in medium-size saucepan over medium heat. Add garlic and onion; cook for 8 minutes or until softened. Stir in vinegar, lemon juice, hot sauce, ketchup, mustard and cayenne. Simmer, covered, 15 minutes. Remove from heat; let stand 20 minutes or until cooled.
Place meat in roasting pan. Brush both sides of meat with sauce, spooning any remaining sauce on top. Cover; refrigerate overnight.
Heat oven to 350 degrees F. Bake meat, covered, for 2 hours. Reduce oven temperature to 250 degrees F; cook 6 hours or until fork-tender.
Slice meat against grain. Serve with bottled barbecue sauce (or your favorite recipe) for dipping. Makes 16 servings.