Eldarion is mentioned briefly (just that he was the king at the time) in "The New Shadow" (Tolkien's attempt at a sequel for LotR) and the commentary about it from Christopher Tolkien, in "The Peoples of Middle Earth". Tolkien kept changing his mind about the timing, in other words how long Eldarion reigned. But, as far as I can tell there is nothing describing his character as a person.
--Imladrien
Reading Tolkien's Middle-earth