There were at least 2 sci-fi stories written in monologue-- perhaps just first person narrator. Both were single men, telling the stories of how they got where they were.
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One, man on the moon keeping watch over a nuclear weapon stockpile, slowly dying of the radiation he was exposed to. He was dedicated to civilization and preventing its destruction. One of the golden age authors. Heinlein maybe?
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Two, a man on a space station outside the orbit of Pluto, running the terminus of an interstellar transport network. "The Second Kind of Loneliness" by George R.R. Martin - from the December 1972 Analog science fiction magazine. Kelly Freas cover.
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Both stories may have had a final postscript paragraph not part of the monologue.
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Side note-- most surprising thing about artist Kelly Freas is that he created some of the most iconic images of the 1960s-- covers of Alfred E Neuman for MAD Magazine. He also did some nice portraits of the stars of the original Star Trek.