Heat gas or charcoal grill for indirect grilling as directed in owner's manual. Remove and discard neck and giblets from turkey. Rinse turkey with cold water. Season cavity of turkey with seasoned salt and pepper. Fasten neck skin to back with skewers. Turn wings back and tuck tips under shoulder joints. Refasten drumsticks with metal piece or tuck under band of skin at tail. Rub outside surface of turkey with oil. Insert meat thermometer so tip is in thickest part of thigh and does not touch bone.
Place turkey, breast side up, over unheated side of grill directly over drip pan. Cover grill; cook turkey with medium heat 2 1/2 to 3 1/2 hours or until thermometer reads 180°F to 185°F and legs move easily when moved or twisted. Avoid lifting cover until ready to check thermometer. (There is no need to baste or turn turkey.) Let turkey stand 15 to 20 minutes before carving.