Something about the way Buffy said 'don't be silly' made Eliot smile a little. The idea that he'd be silly to leave just because she was in a meeting was... it was nice.
And her watcher no less.
"You're watcher?" He asked, wheeling himself over to the desk. "It's good ta meet you to. It's been a long time since I've met a Watcher an' Buffy's told me a lot about you." Not told in the strictest sense but he wasn't getting into that mess now.
He turned to Buffy. "You tell him 'bout this End of Days yet?" A glance back toward Giles later he added. "Though if you told him I was Eliot an' all he has to say is it's good the teams growing I'm gonna take that as a no." It wasn't egotistical. If you were a necessary part of starting the apocalypse he doubted others would comment on how happy they were you joined the team.
He turned back to Giles with an expression that was somewhere between rueful, resigned, bitter, and 'life is so far past the 'oh crap' stage you have to find it kind of amusing' on his face as he held out his hand like he was offering to shake hands and said. "I'm Eliot Spencer, Retrieval Specialist, one of the Two Witnesses, a herald of the apocalypse. It's nice ta meet ya."