IIRC,it's called a " windshield pump squirter nozzle" . A bit of advice: Take lots of pictures, before disassmbly. Would save you ,lots of answers,in the long run.
It looks like you have it backwards/up side down. They are supposed to point AT THE WINDSHIELD, not the engine. (unless your engine has overheating problems...)
Another member was trying to find a small water leak to his interior. He found that after deleting the window washers the screw hole for that 'T' ( or actually 'F' ) connector allowed water to drip into the left vent box.
The one that is laying in place in your picture goes on the other side, and the tube sticks up between your cowl vent strips so it can spray water on the windshield.