[link to original on tumblr]
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I'd previously noted the alliteration in that second line ("For fussing and fighting my friend"), but the "my friend" part stuck out in listening to it this time. Writing it out, it could be either "For fussing and fighting my friend" or "For fussing and fighting, my friend." In the first, "friend" is the object of "fighting;" in the second, "friend" is a vocative - the person to whom the whole statement "Life is very short, and there's no time for fussing and fighting" is directed.
It reminded me of an-other ambiguous "my friend" I discovered in the Beatles' catalogue. In the first verse of "I'm a Loser" from Beatles for Sale, there's the line: "She was a girl in a million, my friend." Here, it could be a vocative (someone to whom "She was a girl in a million" is directed) or an appositive renaming the "girl in a million" (which could be rendered as "She was a girl in a million [and] my friend"). I think it makes more sense as a vocative, but it's still viable as an appositive.