Here's an episode from Homer's Odyssey, the story of Odysseus's journey home to Ithaca after the Trojan Wars, that seems to me very like a Third Man incident.  

Odysseus builds himself a raft so that he can sail off from the island of Ogygia (book v lines 228-61). He sails alone for eighteen days (279). A massive storm blows up, and Odysseus fears he will be drowned (291-312). He is swept from the raft and dragged underwater, but manages to crawl back onto the raft and hang on (313-32). At this low point, a figure appears on the raft and tells him how to escape his predicament -- he needs to abandon the raft and swim for it (332-50). As his raft disintegrates Odysseus swims away -- swims for three days -- and finally reaches solid ground and safety (374-463).

So, what we have here is a single-handed sailor, alone for three weeks, now in a life and death crisis; a figure appears and tells him how to escape. 

Online version of an old translation of this passage as part of the Perseus project, here: http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0136%3Abook%3D5%3Acard%3D228

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I've paraphrased the episode, to bring out its resemblance to a third man episode -- I'd obviously not have thought of reading it in that light before reading The Third Man Factor. A more neutral retelling of the episode would be this: 

Odysseus is on his raft, when Poseidon (his implacable enemy) sends a storm to destroy him. A sea nymph, Ino, swims up and sits on the raft, and tells Odysseus that he should strip and swim for it, and gives him a divine veil that will keep him from harm (349-50) -- once he is on land he needs to throw this back into the sea. Odysseus is suspicious and decides to stay on his raft for as long as he can, and only begins to swim for it when Poseidon smashes his raft. Then he swims. When he finally gets to dry land he throws the veil back (459).

The fact that the mysterious figure is a sea nymph renders the episode unremarkable in the Odyssey, in which mysterious figures do turn out to be major or minor divinities. And the fact that Odysseus decides that he knows best, and only goes to swim at the last moment, is typical of him in the poem. And I suspect that a good part of the motivation for this slightly ill-fitting episode is the fact that it is essential that it is very clear that Odysseus is naked when he finally gets to land (because the next episode is the light comedy of an unclothed Odysseus meeting Princess Nausicaa). All of which being the case, this episode still looks like a nugget of folk tale, tailored for a specific use here. 

One way in which this episode is ill-fitting in its context is that, as Odysseus swims to land and is about to be dashed on some rocks, the goddess Athena twice saves him from being smashed on the rocky shore (427, 437). The Ino episode becomes somewhat superfluous. It is much more appropriate that Athena help Odysseus, because he is her favourite, and throughout the Odyssey she assists him in his journey home, just as the angel Raphael assists Tobias in the book of Tobit.

I file these episodes under "literary appearances" because they appear in the Odyssey. But, clearly, the Odyssey is a product of a long mythological and folkloric tradition, tales of importance to the people who swapped them. Given that, and in the light of the phenomenon of the Third Man, I begin to wonder whether the appearances of Io, or Athena, are not narrative devices (revealing what Odysseus should do next), nor facets of an imagined world (simply invented for this episode), nor even simply reflections of the cosmology of the Homeric age, but reflect the experiences of real Greek sailors and travellers, through the prism of folklore and myth, and preserved for us in the Odyssey.