Whisk together all ingredients in a medium bowl and season with salt to taste. Truss the turkey. Place turkey on a work surface, breast side up. Rub it with olive oil, and season with salt and pepper. Heat the grill to medium heat. Have the rotisserie shaft fitted with 1 spit fork. Making certain that the turkey is centered, push the rotisserie shaft through the turkey between the legs, exiting at the neck. Slide the spit fork onto the shaft. Insert the tines of the spit forks into the turkey, screw side up, and tighten the screws to secure firmly. Set the rotisserie shaft in place in the rotisserie ring. Loosen the retaining loop at the handle, and let the counterweight assembly hang down to counterbalance the weight of the breast. The rotisserie should rotate so that the heavy side of the turkey rotates down to the bottom. Swing the counterweight assembly so that the counterweight is directly opposite the heavy side of the turkey. Tighten the retaining loop. The counterweight travel should stick out a little bit above the shaft handle and retaining loop. You may need to adjust the travel of the counterweight as the food cooks, or if the motor sounds like it is straining. Insert the pointed end of the rotisserie shaft into the motor. Set the rotisserie shaft into the ring. Cover the grill, and turn the motor on. Grill the turkey 11 minutes per pound if unstuffed. During the last 30 minutes, baste the entire turkey with 1 cup of the marinade. Remove the turkey from the grill and immediately brush with the remaining glaze. Let rest for 20 minutes before slicing. To determine if the turkey is thoroughly cooked, insert an instant-read thermometer into the thickest part of the inner muscle of the thigh, making certain not to touch the bone, and check that the temperature is 175 to 180 degrees F.