Trim fat cap to 1/4 inch. Place brisket into a large foil pouch and pour in vinegar mixture, 1/4 cup Worcestershire sauce, and 1/4 cup honey. Place pouch in smoker and cook for 6 hours, changing chunks as needed.
Remove brisket from pouch, spread mustard evenly on it, and massage Rub into meat. Place brisket back into smoker and cook for 10 hours, changing chunks as needed.
Separate brisket halves along fat line. Slice across the grain as thinly as humanly possible, chop roughly, and place serving portion in halved buns.
Place some vinegar mixture into a squirt bottle and serve with sandwiches.