At any moment he was willing to divulge information about himself, yes. I was amused to find he had ties to that Emiya Shirou boy.

[ And by "amused" she means she laughed in his face and congratulated him on growing a brain. Meanwhile, Caladbolg is going to mosey between Arturia's legs and rubbing his head against her shoes while Hydra rolls on her back. ]

And I wished to confirm the events that happened between our Master. In one parallel, he is the Servant to my Master, instead of me. Even without him recalling his account, his words confirmed my own victory.