Whisk together the ingredients for the marinade, and season to taste.
Make three deep slits into the turkey drumsticks, then rub the marinade into the turkey.
Place in a sealed Ziploc bag and marinate overnight, or for at least 4-6 hours in a refrigerator.
When ready to grill, bring the marinated turkey drumsticks back to room temperature.
Preheat the barbeque to 450F (230C). Brush the grill with a little oil.
Turn down the barbeque to 400F (205C), and grill the drumsticks for 25-30 minutes (depending on the size of your turkey drumsticks), turning a couple of times, and brushing with oil, until the juices run clear and the turkey is cooked all the way through.
Rest the turkey for a few minutes before shredding the meat off the drumsticks, and serving over the mushroom pilaf and a few lime wedges.