Who is The Deathless Man (Gavran Gaile) from The Tiger's Wife: A Novel and what is their importance?

The "Deathless Man" appears in stories told to Natalia by her grandfather. The Deathless Man never ages, he claims to be the nephew of Death, and he claims to have been given the ability, following a complex ritual involving coffee drinking and the reading of its dregs, to know when/whether people are going to die. The character is described as matter-of-fact, compassionate, wise, patient, and tortured... a man cursed by his uncle, to remain alive forever.