It's likely that the o-rings on the eagle hitch piston are leaking/failing. That piston is embedded in the top plate for the transmission (see diagram). Remove the piston based on the service manual instructions below, and replace the o-rings and steel wiper rings if so equipped.
NOTE: Do not order parts until you get the piston assembly out and inspected. Case made several different styles of pistons. One series had only two o-rings. One had a single o-ring with two steel wiper rings. One had a plastic wiper and a o-ring..... you get the point. It's like Forrest Gump's box of chocolates, you wont know what you have until you get it opened up. The piston depicted here is the early, two o-ring setup. Yours likely left the factory with a single o-ring and two steel wiper rings (one on each end, with the o-ring in the middle). However, who knows what might have been swapped-out in the past 50 years. There were several service bulletins on that assembly over the years.