Typically a "midship" fire pump is designed to operate in the highest transmission gear. The transfer case engages the pump and disengages the the drive line from the rear axle (thus the need to positively set brakes). The pumper is NOT designed to drive with the pump engaged.
The small pump unit on the side of the transfer case might be a primer pump. If so this is a "positive displacement" gear pump which will pull a vacuum. These usually have some oil feed with a small reservoir up "high". Use of the primer allows water to be pulled up a suction hose to the main pump enough so it will begin moving water. (Yes, technically the water would be pushed by atmospheric pressure).
The common operating procedure would be:
Stop the pumper. Set brakes.
Clutch in, transmission to neutral, shift to pump, transmission to high gear, clutch out. Throttle at idle.
Step outside. Chock wheels.
If you have a water tank (and many pumpers of that era did not) make sure all intake valves and discharge valves are shut and ports capped. Open tank to pump valve. Uncap and open one discharge port slightly. Increase RPM and operate primer until water is showing at discharge port. Now you can connect a hose or switch to another port and adjust RPM to achieve the desired discharge pressure. If you are not flowing water you can reduce RPM to idle and open a tank to pump valve to circulate water to keep the pump cool (running with the pump engaged and not flowing water can overheat the pump).
If you are getting water from a hydrant or other pressurized source you may not need to use the primer. Open the appropriate intake valve and slightly open an outlet valve and wait for water to show. (DO NOT USE SUCTION HOSE ON A HYDRANT, bad things to a water system can happen).
If you are going to suck water from a static source you will need hard suction hose, and all hose gaskets (and your pump, valves, and pipes) will have to be in good condition to avoid air leaks. You want a strainer and some means of keeping the strainer above the mud level of what you are pumping from (often the suction hose is tied to a ladder). (Sidebar... wading chest deep into a mill pond to tie off a suction hose is not a fun thing.) Those big lugs on the inlet side of the pump... thats so you can use a rubber mallet to try to get a good seal on the suction hose. With the discharge ports closed and the inlet open pull on the primer pump, this may take a few minutes. You should notice a vacuum indication on the inlet pressure gauge, then the suction hose filling with water and a change of sound of the primer pump as water fills the main pump. When you see pressure on the outlet gauge then slightly open a discharge port, if you have water showing then open it slowly until you have water freely flowing... now you can pump through whatever hoses you want to.
