Mix brown sugar, garlic powder, onion powder, paprika, seasoned salt, black pepper, cumin, and cayenne pepper together in a small bowl to make dry rub.
Coat roast with spicy brown mustard. Sprinkle dry rub all over roast and work it into all the folds and creases.
Combine pickle juice and olive oil in a small bowl.
Preheat 5 pounds charcoal in a smoker according to manufacturer's instructions until white and flaming. Distribute 7 to 8 large wood chunks over the coals. Place a drip pan on top; pour in beer and enough water to fill the pan most of the way. Close smoker; bring liquid in the drip pan to a boil. Place roast on top and close smoker.
Smoke roast, turning every hour, until browned, about 2 hours, adding wood chunks as needed to maintain the temperature at 350 degrees F (175 degrees C). Baste roast with pickle juice and olive mixture. Continue smoking, turning, and basting every hour, until an instant-read thermometer inserted in the center reads 175 degrees F (80 degrees C), 2 to 3 hours more.
Remove roast from smoker and wrap with aluminum foil. Let rest, about 30 minutes.
Uncover roast and cut into chunks. Shred chunks into small strands; transfer to a large bowl. Squeeze strands with both hands repeatedly, mixing after each squeeze.