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Add garlic mixture to goat, and stir to coat goat in garlic mixture.

Halve onion lengthwise; reserve one half for another use.Slice remaining half lengthwise into two wedges; set aside.

In a large skillet, toast guajillo and arbol chiles over medium-high heat, turning occasionally, until fragrant and pliable, 2 to 3 minutes.Stem chile mixture and halve lengthwise.Remove and discard seeds and ribs.. Place chile mixture and tomatoes in a large saucepan and add just enough water to cover.

Bring chile mixture to a boil over high; reduce heat medium, and simmer, adjusting heat to maintain a simmer, for 10 minutes.Remove pan from heat, cover, and let soak until chiles feel soft and pulpy, about 10 minutes..

Drain chile mixture, reserving 2 cups cooking water.

Place chile mixture, reserved 2 cups cooking water, and garlic in a blender, and remove center piece to allow steam to escape.Using your hands, slather the entire surface of the chicken with the marinade.

Allow the chicken to marinate at room temperature while you prepare the grill; alternatively place the marinated chicken in a large resealable plastic bag.Seal the bag and transfer to a baking dish.

Refrigerate up to 12 hours.Bring chicken to room temperature before grilling, about 1 hour.. Preheat a gas grill to medium-high (400°F to 450°F) on 1 side, or push hot coals to one side of a charcoal grill.