My April, '31 deluxe roadster has a full width bumper. I believe it is original to the car because the rust on it matches the rusty front bumper!
The
June, 1929, Ford Service Bulletin shows a pic of a closed car with the new truck rack on the back. With a full rear bumper and the proper '29 center clamp. Nothing in the ad. is mentioned about the rear bumper though.
Bob-A