This was a manual 'stick shift' transmission that had a 'strange' shifting mechanism as Chuck said. As I recall it had one shift rod that slid in/out for selection and rotated to change gears.
The Hydra-Matic can be beefed up to work great and was used on many a drag strip, way back then.
Go with a 4 speed Muncie or the T-5 as like he said. You can't go wrong.
