Three things, each as important as the other.
Klaus doesn't know the story between him and Pickle Berry, so it was only natural to assume it wasn't a simple one.
He wanted to find out why he felt such a strong attachment to a mere snake. He most certainly didn't know why or what could have happened between him and the snake to face the heavens in the end.
The story between him and Pickle Berry is one he must know.
Although he doesn't know yet, the just-ended battle between him and the heavens was because of Pickle Berry. They didn't want her alive, for she knew too much.
He didn't know that, but he could feel it, and as such, he wanted to know why.
But then again, there is the Awakening.
It was something Klaus had already started planning for. If anything, he most certainly would want to know something about it.
