Examine the turkey tails closely. Utilize a paper towel to get a better grip and pull out any feather shafts you may find.
Combine the soy sauce, honey, water, 2 teaspoons of turkey rub and garlic in a bowl. Stir until combined. Place the turkey tails in the bowl and make sure they are evenly coated with the marinade. Cover with plastic wrap and refrigerate for at least 4 hours or overnight for best results.
Drain the marinade from the turkey tails and pat them dry with paper towels. Combine 1 teaspoon of the turkey rub, dijon mustard, vinegar and garlic in a separate bowl. Place the turkey tails in a shallow dish or roasting pan and pour this mixture over top. Ensure that all of the turkey tails are evenly coated.
Preheat your smoker to 225°F. Place the turkey tails on the top rack and cook for 30 minutes, or until the internal temperature is 160°F. Baste with remaining marinade halfway through cooking.
When done, remove from heat and let cool before serving.