Pat the goat meat dry with paper towels. In a bowl, combine the salt, pepper, garlic powder, smoked paprika, brown sugar, cumin, and chopped thyme.
Rub the dry spice mixture all over the goat meat. Let it rest for at least 2 hours, or preferably overnight, in the refrigerator.
Preheat your grill or smoker to 250°F (120°C). Prepare the charcoal or smoking wood for an authentic BBQ flavor.
Place the goat meat on the grill grate and smoke or slow-cook for 3-4 hours, or until the meat is tender and easily pulls apart.
In a bowl, mix together the Worcestershire sauce, apple cider vinegar, and BBQ sauce. During the last 30 minutes of cooking, brush the goat meat with the sauce mixture to add extra flavor and a glossy finish.
Once cooked, remove the goat meat from the grill and let it rest for 10 minutes to allow the juices to redistribute throughout the meat.
Slice the goat meat and serve with grilled vegetables, a fresh salad, or roasted potatoes.
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