Stir together all rub ingredients in a bowl. Store in an airtight container. Set aside.
Stir together all ingredients for the sauce in a medium saucepan over medium heat; bring to a boil. Reduce heat; simmer, stirring occasionally, 40 minutes.
Divide sauce into separate containers for basting and serving at the table. (Basting brushes used on raw food should not be dipped into table sauce.) Use as a basting sauce during the last 10 minutes of cooking for steak, pork, burgers, or chicken. Discard any remaining basting sauce, and refrigerate any leftover table sauce.
If needed, trim the fat back to about 1/8 inch thick on shoulder. Sprinkle meat generously with rub, massaging it into the meat. Wrap tightly with plastic wrap, and chill overnight in the refrigerator.
Smoking a large piece of meat takes a long time, so you'll need to get an early start. Prepare your smoker or grill until the temperature reaches 250 degrees F. Take the meat out of the refrigerator, and let it sit for about 30 to 45 minutes. Having the pork at room temperature is very important, because if you put it on the smoker cold, the outer portion will burn.
Smoke is one of the main ingredients of good barbecue. Soak hickory wood chips (or any other hardwood chips used for barbecuing) in water overnight. This prevents them from burning. The chips smolder, producing smoke that flavors the meat during the cooking process. The smoke also lends a pink color to the outer inch or so of the flesh, creating what is called a smoke ring. A handful of wood chips should be added to the fire every 30 minutes or so. The more you add, the stronger flavor of smoke you get.
Place meat on the smoker fat side down. After two hours, turn the meat over so it is fat side up. Total cook time will be 1 1/2 hours per pound. Maintain the temperature in the smoker between 225 degrees F and 250 degrees F. Use a pit thermometer for an accurate reading. If the smoker temperature is hotter than 250 degrees F, the meat will cook too quickly; any lower than 225 degrees F, and the meat will not get done. Every time wood chips or charcoal is added, spritz the meat with apple juice from a spray bottle. This will add moisture and a fruity background flavor during cooking.
Remove the meat from the smoker with two hours remaining, and place on heavy-duty aluminum foil. Spritz generously with apple juice, and tightly seal foil around pork. Place meat back on the smoker, and cook for two hours more. Using an instant-read meat thermometer, check the internal temperature of the thickest part of the meat, being careful not to touch bone with the tip of the thermometer. When the internal temperature reaches 195 degrees F, the pork is ready. Cooking the meat beyond the USDA guideline of 145 degrees F (63 degrees C) renders out the fat and tenderizes the meat.
Remove the meat from the smoker, and let it cool for 15 to 30 minutes. Remove foil after it has cooled enough to handle. Remove the bones, which will easily pull away. Begin pulling, or shredding, the meat with two large forks, and place in a large baking dish or pan. Remove and discard any remaining fat.
Add the sauce to pulled pork, and toss. This is a popular way to serve pulled pork in most regions. If you prefer, serve with additional sauce.