I think the brass thing is an air vent…if so this is my guess as how the system works:
The submersible well pressure switch is set at a higher pressure than the jet pump pressure switch. The two fiberglass tanks are normally full of water and the automatic air vent will close, causing the fiberglass tanks to pressurize, pushing water through the jet pump satisfying well pressure switch.
When you use water in the house, the well pressure switch will turn on first, if the well keeps up only the well pump will run. If the well pump can’t keep up, the pressure will fall enough causing the jet pump pressure switch to turn on and start pulling water out of the fiberglass tanks, and the air vent will open, and the fiberglass tanks will go to atmospheric pressure.
When you quit using water in the house, the jet pump will shut off first. The well pump will continue to run until it fills the fiberglass tanks back up, the vent closes, the fiberglass tanks pressurize, and water pushes through the jet pump and satisfies the well pressure switch, shutting off the well pump.
I have never seen anything like that set up, but that doesn’t mean it’s a bad thing.
I don’t know what the ticking sound would be.