Mine is not from harbor fright, and it has a little valve at the hose connection that you just open and close. So yes when the valve on mine is open, air is always coming out. Put a little ball valve on it.
The air runs continusly so you'll need a hi cfm compressor to keep up or put a shut off valve inline at the connection fitting. Trigger dispenses material.
You need a shut off valve at the handle to shut the air off. But yes once the valve is open the air flows freely, the trigger is to control the flow of the "mud". I have one from marshall,