Image of an early 1958 water pump, from the 1958 Advance Service Manual for Lincoln (printed Sept. 1957). Note the square plugs which are absent on later designs. I've been searching for an early 58 pump for my restoration and have learned the difference between A/C and non-A/C water pumps was the size of the bearing. Non-A/C had a smaller bearing which went out sooner so it seems that most pumps were replaced with the larger bearing style.
According to the 1958 Merc/Linc service bulletin below, both A/C and non-A/C used the same pump up to April 1958 (EDG-88502-B). This service guide indicates replacing defective water pumps on A/C cars with a new pump 5751567. Non-A/C car pumps could be overhauled and re-used although they could be replaced with the larger bearing type.