I think it is a noun phrase, and not appositive.
Based on the excerpt from Joseph Conrad's "The Lagoon", I think that it takes Arsat all night to tell his story. I have inferred such due to the sentence: "<span>Before his face the sun showed its edge above the tree-tops, rising steadily." This means that the sun has already risen. Arsat told a story about his past wherein he and Diamelen, escaped from the rajah's men. </span>
