I think I see now how this type of thermostat works and why it probably would not work in my 59A. This style is made for the bottom to sit in a large space with the water surrounding it rather than in the neck of the 59A head where the water has to pass by the "cup" on the bottom. It works great for the first environment because when the cup is lowered the water flows unobstructed over it and through the stat. But, in the neck of the 59A head the cup would be obstructing the flow of water unless it extended down into the more open area below the neck. If the cup sat in and then lowered into the narrow neck it would be blocking the flow of water that would have to pass around it on the sides in the narrow space between the cup and the sides of the neck.
Darn, I thought I had something there that would be an improvement for my 59A. I guess that's why that style of stat is not sold for the 59A heads.