In a food processor or blender combine the marinade/glaze ingredients. Process until the mixture is well blended, 2 to 3 minutes.
Place the wings in a large, resealable plastic bag and pour in 1 cup of the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place in a large bowl, and refrigerate for 2 to 4 hours, turning occasionally.
Pour the remaining marinade into a small saucepan. Bring to a boil over high heat. Continue to boil until the liquid is very slightly thickened and reduced to a scant 1 cup, 8 to 10 minutes, whisking occasionally and lowering the heat if necessary so it doesn’t burn. Remove from the heat. Transfer ½ cup of the glaze to a small bowl for brushing on the wings at the end of grilling. Reserve the remaining glaze in a separate bowl for serving alongside the wings.
Prepare the grill for direct cooking over low heat (250° to 350°F).
Remove the wings from the bag and discard the marinade. Season the wings with the pepper.
Brush the cooking grates clean. Grill the wings over direct low heat, with the lid closed, until the meat is no longer pink at the bone, 20 to 25 minutes, turning occasionally and watching closely to avoid over browning. Brush the wings with the ½ cup reserved glaze during the last 5 minutes of grilling time. Remove from the grill and serve the wings hot with the reserved glaze alongside for dipping.