Make the brisket: Mix the paprika, brown sugar and 2 tablespoons each salt and pepper in a small bowl. Rub and pat all over the brisket in a thick even coating. Cover with plastic wrap and refrigerate overnight.
When ready to grill, soak the wood chips in cold water in a large bowl. Prepare a charcoal grill for indirect cooking: Light the coals, then bank them to one side of the grill. Set up a drip pan on the other side of the grill and replace the grates. Let the fire burn until the temperature is between 200 degrees F and 250 degrees F (you should be able to hold your hand about 5 inches away from the coals for 6 seconds). Drain the wood chips and scatter a handful of them over the coals. (If using a gas grill, cook over low indirect heat and use a smoker box for the wood chips.)
Place the brisket fat-side up on the grates above the drip pan. Cover the grill; adjust the vents to maintain a temperature between 200 degrees F and 250 degrees F. Cook until a thermometer inserted into the thickest part of the brisket registers 185 degrees F to 200 degrees F, 7 1/2 to 10 hours. Rotate the brisket every few hours and add more charcoal and wood chips every 45 minutes to keep the temperature steady (use dry wood chips if you need more).
Remove the brisket from the grill, wrap in foil and let rest 45 minutes to 1 hour. Pour the drippings from the drip pan into a bowl; let them settle, then skim off the fat.
Meanwhile make the sauce: Combine the vinegar, ketchup, brown sugar, Worcestershire sauce, hot sauce, paprika and 1 teaspoon salt in a saucepan over medium heat. Cook, whisking, until hot but not boiling, about 3 minutes. Let cool; season with salt.
Slice the brisket against the grain. Serve with the pan juices and sauce.