Fire trucks operated their pumps by disengaging the rear wheels from the transmission, and engaging the fire pump to the transmission. In other words, the drive shaft went through the pump transmission. When they drove, the transfer was in "Road", and when they pumped, the transfer was in "Pump". When the fire truck got to a fire, the driver would put it in neutral, push the clutch in, shift from Road to Pump, then shift into 4th or 5th gear, before letting the clutch out. The pump operated through the transmission, usually in whichever gear was "direct".
However, all the pump controls on a fire truck are usually on the side. So after putting the pump in gear and getting out of the truck, the engineer needs a way to disengage the pump, without having to climb back into the cab.
By flipping a switch on the pump panel, vacuum would be allowed into the canister, which, acting on the piston inside, would pull that cable attached to the bottom of the clutch pedal, thereby disengaging the clutch. In this case, that would allow the pump to stop pumping, or "shut down". There is also a remote throttle control on the panel for adjusting the speed of the engine. If they weren't going to pump for a while, the driver could then climb back into the cab, take the transmission out of gear, and idle the engine.
If you aren't going to return this truck to a fire truck, I can't imagine what use the vacuum clutch control would be to you. It doesn't have any effect on your driving the truck. No reason not to remove it and the associated plumbing - just be sure to plug it at the source, to avoid a big sucking vacuum leak!
-Michael
