I think he probably is talking to himself(stinker-slinker),because if he was talking to Frodo, then it would mean that Frodo was telling Gollum those things and being kinda mean to him. Frodo was hardly ever being mean to Gollum in the movie, and if the song was written for the movie, then it wouldn't make much sense.(If you get what I mean).
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"They do not see what lies ahead, when sun has failed and moon is dead."
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