For marinade, in bowl whisk together tequila and oil. Whisk in honey, lime juice, peel, salt, and desired add-ins. Cover and refrigerate marinade up to 2 days.
Place drumsticks in a self-sealing plastic bag set in shallow dish. Add marinade; seal. Refrigerate 4 to 8 hours, turning occasionally. Drain; discard marinade.
For charcoal grill, arrange medium-hot coals around drip pan. Grill drumsticks 50 to 60 minutes over drip pan, covered, until chicken is no longer pink (180 degrees F), turning once halfway. (For gas, heat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as above.) Makes 6 servings.