"I just... like... time," the Doctor explains, not at all awkwardly, when Rei asks why. Well, Time Lord, it does stand to reason, and if he's lucky, sooner or later Rei will just decide he's a bit mad anyway. People tend to stop questioning you after that.

He takes the watch from Rei gently, pointedly careful with it - if it is a chameleon arch, there's good reason for that, and even if it's not... well, Rei is a bit too protective of it for an ordinary watch. But as he turns it over in his hands, his first guess seems less likely. No Gallifreyan writing anywhere on the thing, nothing terribly out of the ordinary that he can see - or sense, for that matter.

Glancing up briefly to Rei, he frowns for a second, and decides to take a chance opening it. Though he's braced to snap it shut right away should it start glowing or anything, nothing strange happens then, either. Not a chameleon arch, then. Not a Time Lord in disguise.

Good, he thinks, though there's a small part of him inexplicably disappointed. With my luck, he'd have been the Master. Again.

The Doctor studies the watch a moment longer before closing it gently and offering it back. "Shame it's broken," he remarks innocently. "It's a lovely watch..." Which, now that he thinks about it, still doesn't explain Rei's attitude about a more or less ordinary fobwatch. Odd, that.