Sprinkle each side of beef with 1/4 cup Brisket Rub; rub thoroughly into meat. Wrap brisket in plastic wrap, and chill 8 hours.
Soak hickory chips in water for 8 hours. Drain.
Prepare smoker according to manufacturer's directions, regulating temperature with a thermometer to 225°; allow it to maintain that temperature for 1 hour before adding beef.
Remove beef from refrigerator, and let stand 30 minutes.
Place brisket on smoker rack, fat side up. Insert thermometer horizontally into thickest portion of beef. Maintain smoker temperature between 225° and 250°.
Add a handful (about 1/4 cup) of hickory chips about every hour.
Brush beef liberally with Brisket Mopping Sauce when beef starts to look dry (internal temperature will be about 156°). Mop top of brisket every hour. When internal temperature reaches 170°, place brisket on a sheet of heavy-duty aluminum foil; mop liberally with Brisket Mopping Sauce. Wrap tightly, and return to smoker.
Remove brisket from smoker when internal temperature reaches 190° with an instant-read thermometer. Let stand 1 hour. Cut into very thin (1/8- to 1/4-inch thick) slices. Serve with Brisket Red Sauce, if desired.