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not sure why no one answered. i just stumbled on this post as I'm looking for similar questions. it seems that some owners used to disconnect the second hose to have the engine run cooler while idling.
The black hose in the pic is the distributor advance vacuum line and is required. The nipple without a hose in the pic would normally be the distributor retard hose, but yes many people disconnect it. In fact, many distributor pods(like mine) don’t even have the second connection.