Somewhat hard to tell from the picture, but I believe that truck has a Barton American Pump, and would be manufactured by American Fire Equipment. I believe the main factory was in Battle Creek Michigan. Wise American Fire Equipment out of Salina Kansas, Now Wise Fire Equipment, sold them by the train load to almost every fire department in Kansas.
There were either 500gpm pumps with 2 outlets or 750gpm pumps with 3 outlets. The pumps were driven from the front of the motor, and were capable of pump and roll. Many chassis were used not just Ford, also Chevy, GMC, and International. Almost all were prone to overheating, since the factory crimped off the bottom 6 to 8 inches of the radiator for the pump drive shaft to go through it.
They had Vacum primer and a crude pressure governer, neither of which worked for long.
I believe that Barton American was bought by Hale, parts can still be had, but are custom made.
Many of the trucks were built in Michigan then shipped uncompleted to Salina where Wise American would finish them. They would Install the lighting and switches, the hose bed racks, and outfit the truck with its final equipment. Most everything was Federal Signal equipment. Many departments here also purchased their truck locally, had it shipped to michigan to be upfitted, then either drove them back or had them shipped back to Salina where they were finished.
This one would be a later truck and a very highly spec'd truck too, most here had only single or dual beacons, not full lightbars. Im guessing it also has a PA-20 siren, most everyone of them I have ever see have been that way.
A department I was on had a 1970 Chevy C50 that was pristine with 1200 miles on the odometer, a 500gpm pump, and Federal model 14 beacon on top. We sold the truck for $500 when it was replaced.