I’d been interested in the origin of the term “eidolon” after hearing the Let’s Talk About Myths, Baby episodes on Euripides’ Helen, and remembering that the term had been used in the Final Fantasy series.
It’s basically a phantom, a duplicate of a real person made of clouds, or something of the sort. The most famous occurrence of the term is in relation to Helen of Troy. Basically, the premise of the play is that Helen, despite the appellation she’s generally given, never actually went to Troy. It was presumably at least partially an attempt to rehabilitate the character. Whether or not she chose to go with Paris to Troy, and hence whether she was complicit in the subsequent war, was a point of contention for people writing about the Trojan War.
Euripides’ version essentially makes the argument irrelevant. The real Helen was taken by Hera and Hermes to Egypt for the entire length of the war. Euripides was apparently working from an existing tradition, as Herodotus also mentioned Helen being taken to Egypt, although in his version she ended up there because Paris was blown off course, which means the real Helen did go with Paris but didn’t stay with him. I guess the fake Helen looked identical to the real one, so she’d still technically be the most beautiful woman in the world as per Aphrodite’s promise. The reason Hera had Helen spirited away might have been her way of getting back at Aphrodite, although it would also be a rare case of the Queen of Olympus actually helping her husband’s illegitimate child. That is, unless she wanted to go with Paris, I guess. The fact that goddesses were often mistreated by their male counterparts doesn’t generally seem to have given them any sympathy for the similar plight of human women. The eidolon apparently had a physical component as well, especially if these authors went along with the idea that Helen bore several of Paris’ children. Then again, the centaurs (aside from Chiron) were born when 
It’s thought that the idea might have originated with a poet named Stesichorus, but all we really know is that a fragment of something he wrote says that Helen never went to Troy; I don’t know whether Egypt or eidolons were involved at all. There’s a general idea that, since Helen wasn’t in Troy, the war was fought for nothing. While it’s definitely a valid metaphor for war in general, I’ve seen it said that the Greeks didn’t fight so much for Helen herself as for Paris’ breach of hospitality, which happened even if he ended up with a fake. And the whole thing is kind of Aphrodite’s fault anyway.
Still, Helen didn’t exactly have it easy in Egypt either. The story has it that this nation was ruled by a king named Proteus, who protected Helen. This was presumably not the same as the shape-shifting sea god Proteus, but both are said to live in Egypt, so maybe there’s a connection. When he died, however, his successor Theoclymenos tried to force her into marriage. She and Menelaus, who had been shipwrecked in Egypt, had to trick him into letting her escape. The ancient Greeks didn’t seem to have much knowledge of the rulers of Egypt, if Herodotus was any indication. He was apparently vaguely aware of the names Kheops and Ramesses, but not of who they were and when they ruled. I’m reminded of how the movie The Ten Commandments not only identified the unnamed Pharaoh of the Exodus as Ramesses II, but made him a contemporary of Priam of Troy. While the historicity of the Trojan War and Exodus are very much in doubt, Ramesses’ reign was roughly in the same time period as when what’s been identified as Troy VIIa is estimated to have been destroyed, so why not? I don’t really know why Helen’s place of refuge was Egypt, but the Odyssey does have a mention of her and Menelaus visiting there (as well as Crete, Cyprus, and Phoenicia) after the war.
This whole thing barely scratches the surface of the strange traditions that developed around Helen.
She was worshipped in a few places, including the island of Rhodes, specifically as the tree goddess Helen Dendritis. The story as told by Pausanias is that she was banished from Sparta after Menelaus’ death, and invited by Polyxo, Queen of Rhodes, to live there. Polyxo secretly blamed Helen for her husband’s death in the Trojan War, however, so she had the Spartan woman hunted down and hanged from a tree, or she hanged herself to get away from the mob. It kind of sounds like that was an attempt to tie the familiar Helen to another deity of the same name, but I’m hardly an expert on the subject. Another tradition holds that she and Menelaus were buried in Therapnae in Laconia, where there was a site dedicated to her. I suppose her being revered as a goddess isn’t that strange when her brothers, the Dioscuri, also were. And some tellings of her past make her the daughter of a full goddess, Nemesis, rather than the mortal Leda.
Another account has Helen marry Achilles in the afterlife, which has definite “pair up the main male and female characters” energy to me, like when people wanted Harry Potter to hook up with Hermione (which, incidentally, was the name of Helen and Menelaus’ daughter).
VoVatia 