Who is The Man with One Story from The Piano Tuner and what is their importance?

The Man with One Story is a man called Ibrahim who once worked as a deckhand on a ship travelling in the Red Sea. The ship was wrecked and Ibrahim was washed up on the African shore. He followed two goatherds to a huge encampment in the desert, where he encountered a strange vision of a woman in red. The woman lifted her veil and appeared to have a deer's nose and mouth, with soft fur covering them, but a normal woman's eyes. She sang for him, and the music was so enchanting that it made him deaf. He woke up by the Red Sea and was taken aboard an Alexandrian merchant vessel. He does not believe he dreamt the whole thing, as twenty days had passed since the storm in which he was washed ashore.

Now he travels on this same ship, always disembarking at Aden, as if waiting to see the woman or hear the music again. He says that this is his One Story, as it is the only important thing in his life now. Later, Edgar finds out that he has told a different story to others, this time about the Greek War of Independence. Edgar does not know if he is the only one who Ibrahim told the desert story to, and whether this is the true story of his deafness or not.