I have accidentally stumbled upon an obscure recording of this song that seems to originate from the 40s, but I don't have an exact date for it.
It's performed by Lani McIntire, a legendary Honolulu-born musician who enjoyed considerable popularity from the mid 30s until his death in 1951. He even recorded a few songs accompanying the great Jimmie Rodgers.
It looks like McIntire recorded the song more than once, because if you look at YouTube there's another, better sounding, version of the song by him. This one is also shorter, but it sounds more haunting and appealing to me.
I have also found an image of a 1944 record label that could, or could not, belong to the record I'm posting.
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