1. Submerge wood chips in water; weight with a board or plate. Soak chips for 30 minutes. Drain. Combine brown sugar, salt, garlic powder, chili powder, and black pepper, stirring well. Rub spice mixture evenly over both sides of pork shoulder. Cover loosely with foil; let pork stand at room temperature for 1 hour.
2. Set aside grill rack. Prepare grill for indirect grilling, heating one side to high and leaving one side with no heat. Pierce bottom of a disposable aluminum foil pan several times with the tip of a knife. Place pan on heat element or over coals; add 1 cup soaked wood chips to pan. Place another disposable aluminum foil pan (do not pierce pan) on unheated side of grill. Pour 2 cups water into unpierced pan. Let chips stand for 5 minutes or until smoking; reduce heat to medium-low.
3. Coat grill rack with cooking spray. Set grill rack in place. Place pork on grill rack over indirect heat. Close lid, and grill 3 hours, maintaining a constant temperature of 275°; add 1/2 cup soaked wood chips every 45 minutes. Grill pork an additional 3 1/2 hours or until a thermometer inserted in pork registers 170°. Wrap pork in heavy-duty aluminum foil, and cook an additional 1 1/2 hours or until pork reaches 190°. Remove pork from grill; let stand 30 minutes. Shred.