Summary: The Doctor can make just about any kind of device he needs.
When the Doctor needs a piece of tech that’s never actually been invented, he simply cobbles something together, because he’s brilliant like that. Need to track down someone who’s been zapped into the past? Well then, what he needs is a timey whimey detector, so he builds one.
It’s brilliant, naturally, does exactly what it should. Well, okay, it has a few unintended side-effects, like boiling eggs whether he wants it to or not, but thankfully there aren’t any hens around here so it’s okay. Maybe he’ll fix that when he has time. Right now, he needs to find Billy.