Combine tea, salt, sugar, and pepper in bowl. Pat pork dry with paper towels and rub with tea mixture. Wrap meat tightly with plastic wrap and refrigerate for 6 to 24 hours. Place pork in pan and cover pan loosely with aluminum foil. Poke about twenty 1/4-inch holes in foil. Using large sheet of heavy-duty foil, wrap 2 cups soaked chips into foil packet and cut several vent holes in top. Make 2 more packets with additional foil and remaining 4 cups chips.

For a charcoal grill: Open bottom vent halfway. Light large chimney starter three-quarters full with charcoal briquettes (4 1/2 quarts). When top coals are partially covered with ash, pour into steeply banked pile against side of grill. Place wood chip packets on coals. Set cooking grate in place, cover, and open lid vent halfway. Heat grill until hot and wood chips are smoking, about 5 minutes.

For a gas grill: Place wood chip packets over primary burner. Turn all burners to high, cover, and heat grill until hot and wood chips are smoking, about 15 minutes. Turn primary burner to medium-high and turn off other burner(s). (Adjust primary burner as needed to maintain grill temperature at 300 degrees.).

Place pan on cool part of grill. Cover (positioning lid vent over meat if using charcoal) and cook for 2 hours. During last 20 minutes of grilling, adjust oven rack to lower-middle position and heat oven to 325 degrees.

Remove pan from grill. Cover pan tightly with new sheet of foil, transfer to oven, and bake until tender and fork inserted into meat meets no resistance, 2 to 3 hours. Let pork rest, covered, for 30 minutes. Unwrap and, when meat is cool enough to handle, shred into bite-size pieces, discarding fat. Strain contents of pan through fine-mesh strainer into fat separator. Let liquid settle, then return ¼ cup defatted pan juices to pork. Serve. (Pork can be refrigerated for up to 3 days.).