Combine first 4 ingredients in a shallow dish or large zip-top plastic bag.
Combine seasoned salt, pepper, and paprika; rub into brisket. Place brisket in marinade.
Cover or seal; chill 8 hours, turning occasionally.
Prepare a hot fire by placing 2 pieces of oak or 10 hickory chunks at front and back of grill, piling charcoal in the center. Let burn until coals are white.
Remove brisket from marinade, discarding marinade. Rake coals to 1 side of grill; place meat on other side. Grill, covered, over indirect heat 3 to 4 hours.
Brush both sides of brisket with 1 cup Texas Barbecue Sauce; cook 1 hour, basting with sauce. Serve with remaining sauce. Garnish, if desired.