1. In small bowl, mix salt, thyme, basil, and pepper; set aside.
2. Remove giblets and neck from turkey (refrigerate for use in soup another day). Rinse turkey with running cold water and drain well (do not pat dry). With hands, rub salt mixture over outside and in body cavity of turkey. Place turkey in 13" by 9" stainless-steel, enamel, or glass pan; cover with plastic wrap and refrigerate overnight.
3. About 3 1/2 hours before serving, prepare outdoor covered charcoal grill for barbecuing as manufacturer directs, using indirect-heat method with drip pan (or follow manufacturer's directions if using coverd gas or electric grill).
4. Remove turkey from pan; fasten neck skin to back with skewers. With turkey breast side up, lift wings toward neck, then fold under back of turkey so they stay in place. Depending on brand of turkey, with string, tie legs and tail together, or push drumsticks under band of skin, or use stuffing clamp. Brush turkey with salad oil. Insert meat thermometer into thickest part of thigh next to body, being careful that pointed end of thermometer does not touch bone.
5. Place turkey on grill over drip pan. Cover grill and roast turkey about 2 1/2 hours. Start checking for doneness during last 30 minutes of roasting.
6. Turkey is done when thigh temperature on thermometer reaches 180° to 185°F. and thickest part of leg feels soft when pressed with fingers protected by paper towels. (Breast temperature should be 170° to 175°F.) Remove turkey to platter; let stand 15 minutes for easier carving.