This is a controller for pre 1960 powerflite 2sp transmission. Chrysler used these Torqueflite 3sp transmissions with a button for 2nd gear until 1964  in 1962  they added a park pawl to there transmissions and you would have a lever under the push buttons that would engage park.  Both the park pawl and transmission selector where controlled by cables. Before the park pawl they had a drum brake on the back of the transmission.