These years only had an Engine Number, and the body had a Chassis Number. The Engine Number is also stamped on the top of the Chassis, on the Left Side, just behind the Radiator Support.
The 17 character Numbers didn't start till into the end of the 60's I think.
But, the Engine Number, and Chassis Numbers should be virtually the same.
The Engine Number for a 1960 engine will have a Zero (0) as its' first number, indicating 1960
The Aluminium ID plate on the Firewall gives you the full Body Number.