Rich, a 50's engine most likely has a rubber water pump impeller and should be operated as such. Certainly the impeller should be changed as the material will dry rot.
Some, like the Bendix, Eska, Sears, and small Elgins, are air cooled.
With the vast majority of these older engines, the water pumps were often made entirely of aluminum, or they were a piston driven pump operated off the gearcase, or even a pressure/vacuum system driven off the pressurized water from the propeller blades. The piston driven pumps were a bit more sensitive but these could be run out of water and survive as long as you don't run them for very long. Common sense and feeling the cylinders temp are key.