Neville kept himself busy as Snape processed, not wanting to seem like he was intruding on that moment. Even if he was...less than enthused about the man on the whole, he knew that it was a lot to take in. For him especially.
"I'm here most days." It was information yes, but also an offer, though veiled enough that Snape wouldn't actually have to act on it if he never felt the need. He didn't want to bombard him with the things he would do or live eventually if he didn't want them, especially since Neville wasn't stupid enough to think he had the whole story or that his biases might tint what he chose to bring up. But he also knew enough to understand the things that happened here wouldn't have an effect on their world and it was safe to answer the questions if Snape had them.
He watched Snape leave and let out a sigh, tension he didn't know he was carrying dropping from his shoulders. He decided the rest of his morning's work could wait until after tea and followed him out a few minutes after.