If it cools well with the pressure switch shorted, then yes, it's a bad switch. They have a schrader valve in the fitting so you can just screw it off and screw a new one right back on it. It try to do it with it running because the pressure is lower and you lose less freon if the valve happens to leak a little bit. By the way, it's called a "pressure cycling switch," so you ask for the correct part if you need one.
Good Luck and God Bless
Good Luck and God Bless
