1. Chop anchovies, shallots, garlic and thyme leaves or dried thyme together. With flat side of a knife, press garlic-herb mixture into a coarse paste. Transfer to a small bowl; stir in 2 tablespoons of the wine, 2 tablespoons of the oil and the pepper. Rub mixture over beef. If using fresh thyme, arrange remaining sprigs under string to cover beef. Wrap in plastic wrap. Marinate in refrigerator overnight.
2. Thirty minutes before grilling, unwrap beef onto a large plate. Combine remaining 1/2 cup wine, remaining 4 tablespoons oil and salt in glass measuring cup. Pour half of wine mixture over beef, turning once.
3. Heat grill according to manufacturers directions for indirect medium heat.
4. Sear tenderloin directly over hot coals 15 minutes, turning occasionally. Move tenderloin to middle of the grill. Brush all sides with remaining wine marinade. Cover and grill 50 to 60 minutes more or until meat thermometer reaches 145 degrees F when inserted in center of tenderloin, for medium-rare.
5. Transfer beef to cutting board. Cover loosely with foil; let stand 10 minutes, then slice.