Thank you! This is very helpful. Further information: The hose coming from the bottom of the breather box actually goes along an interesting path and then along side/underneath the right side (non-chain side) of the swing arm, more than half way to the axle, where it is cradled in a u-shaped piece of sheet metal, about 1.5 inches long, which is welded to the exhaust pipe bracket thingie. So.....this hose is 18" long or so and does not drain where the rear tires might otherwise catch the drippings. Engineers are smart. Not all of them, but certainly some. It does NOT have a fish-mouth (excellent descriptive term, BTW). This probably means the box can breathe into that hose.
Follow-up Questions: Does this hose really need a fish-mouth? If so, where could one be sourced? Or how could one be fabricated? What catastrophe will occur if there is no fish-mouth?
Also, as some of you know, I am preparing to synch carbs. I am checking this box as part of my preparations. Is there any reason to feel I need to 'fix' anything related to this breather box before I synch the carbs?