Start your Grill on 'smoke' with the lid open until a fire is established in the burn pot (3-7 minutes). Preheat to 300F.
Using kitchen shears, cut the shell of the tail and crack in half so that the meat is exposed. Pour in butter and season with pepper. Place the tails meat side up on the grill and cook until the shell has turned red and the meat is white, about 35 minutes.
Remove from the grill and separate the shell from the meat. Place the meat in a bowl with mayo, lemon juice and rind and season with pepper. Stir to combine and evenly distribute into the hot dog buns.