The Fool (spoilers for all RotE books, including LST)

[o0Ampy0o]

On one hand, he had failed, but on another he did not. Who says his task was to ensure thriving of dragonkind? Perhaps his final task was to ensure its survival as a species?

Is there any proof that he is as old as the events that tore the world? Or might he have arisen after that? (these beings do not recall that part precisely)

Pilkrop was the only one defining himself as a failure. He may have been wrong but the correction was not made in the story. We were left to think of him as believing himself a failed White Prophet.

A White Prophet does not typically have a clear enough idea of their objective to decide if they have failed, if we are to go by The Fool's example. He often felt like he had gotten many things wrong yet he managed to do a lot. I don't remember whether Pilkrop said he continued to receive ideas about things to do but was unable to follow through on them. In his isolation Pilkrop seemed to have lost the opportunity to inject change, at least until Fitz and The Fool arrived.

He was no match for the Pale Woman. His knowledge of passages into the Elderling cathedral was important though. Before they had known who he was the Fool and Fitz did follow him deeper into the hallways until they were discovered by The Pale Woman. That discovery eventually lead to the explosive freeing of Icefyer and the destruction of the Pale Woman's skill stone dragon.

As a character in this story, Pilkrop did not take a large role in the finale so I do not think he was meant to be a significant participant in The Fool's mission. IOW, it was not a heroic trio that brought the mission to an end. It was a heroic friendship between two characters.