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A classically trained musician, an earlier Zevon song, “He Quit Me,” was featured in the 1969 drama Midnight Cowboy, which he later included on his 1970 debut, Wanted Dead or Alive as “She Quit Me.”
Source: https://americansongwriter.com/behind-the-2003-death-of-sardonic-songwriter-warren-zevon/
So the character Zevon sings about "sinking down" had a lot to do with his real life at the time.