Stuck Cap And Possibly Agitator
Unfortunately during this time period agitators and even the threaded agitator caps often got really stuck when they were never removed for many many years.
Boiling water and or a heat gun will work best, as suggested hold the agitator with your foot and unscrew the cap CCW with your hands [ if it is really stuck you may break the brass stud that the cap screws on to ] If so you will have to get another cap and stud and drill out the brass stud from the steel agitator shaft and re-tap the shaft, this is fairly easy to do.
The next problem may be getting the agitator off the agitator shaft, again a heat gun or lots of boiling water [ several gallons poured slowly over the top of the agitator ] You may also be able to use a puller under the column of the agitator to pull it off.
In many cases again you may not be able to get this agitator off in one piece, luckily they can be broken of the shaft very easily and a standard replacement can be used, but you may lose this cool rare agitator.
Note; unless there is a reason that you have to remove the agitator I might leave it alone.
John L.