Yes it runs through the water jacket. You can get replacement lines which include fittings at about any of the vendors. Jim Carter, The Filling Station, Chevs of the 40s, etc. Since I've not had to actually replace mine I'm not aware of the fitting you refer to. Someone should be along shortly that can help you. Good luck.

Save a life, adopt a senior shelter pet.
The three main causes of blindness: Cataracts, Politics, Religion.
Name your dog Naked so you can walk Naked in the park.