Step 1: Combine the dry rub ingredients in a small bowl and stir to mix. Sprinkle the rub all over the pork, patting it onto the meat with your fingertips. Let the pork cure at room temperature while you make the mop sauce.
Step 2: Make the mop sauce. Combine the vinegar, mustard, water, salt and pepper in a large nonreactive mixing bowl, add 1/2 cup of water, and whisk until the salt dissolves.
Step 3: Set up the grill for indirect grilling and preheat to medium-low. If using a gas grill, place all the wood chips or chunks in a smoker box or smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium-low. If using a charcoal grill, place a large drip pan in the center, preheat the grill to medium-low, then toss 1 cup of the wood chips or chunks on the coals.
Step 4: When ready to cook, place the pork, skin side up, if there is one, in the center of the hot grate over the drip pan and away from the heat. Cover the grill. Cook the pork until darkly browned on the outside and very tender inside, 4 to 6 hours. To test for doneness, use an instant-read meat thermometer: The internal temperature of the pork should be about 195 degrees F. If the pork starts to brown too much (and it probably will), cover it loosely with aluminum foil, but remember that the browned bits are good, too. Every hour for the first 4 hours, swab the pork with some of the mop sauce, using a barbecue mop or basting brush. If using a charcoal grill, every hour you’ll need to add 12 fresh coals and 1/2 cup of wood chips or chunks to each side.
Step 5: Transfer the pork to a cutting board, cover it loosely with aluminum foil, and let it rest for 20 minutes before pulling or chopping. Place the pork slices in an aluminum foil pan. If you are not quite ready to serve, cover the pan with aluminum foil and place it on a warm—not hot—grill or in a low oven.
Step 6: If desired, brush the buns with the melted butter and lightly toast them on the grill. Load each bun with pork and slather with South Carolina Mustard Barbecue Sauce. Top with pickle slices and serve at once.