Last night, as I was reading myself to sleep, I came across a you both. It was in something like We'll leave you both there. Hang on, I thought, how does that work? Under the analysis taken by the Cambridge Grammar of the English Language, the underlined word in I'll leave both there is a determinative functioning as a fused determiner head in a noun phrase. The argument, very much oversimplified, is that the answer to both what is retrievable from context. In other words, if you're talking about pencils, you could say, I'll leave both pencils there.
But there's nothing to retrieve with you both. You can't say, *I'll leave you both people there (not, at least, without changing the meaning), or even *I'll leave you both of you there.
This all occurred to me, as I said, on my way to sleep, so I jotted down a note and resolved to see, in the morning, what the CGEL says. Well, it's now afternoon, but I've finally gotten around to looking it up, and, as usual, they have an answer. They call these universal person pronouns and take all and both to be incorporated into a compound pronoun (p. 427). Others of this form include: us all/both and them all/both.
Seeing this, I now recall reading it before. There's a lot to keep in your head, and unless you use it, you will almost certainly find it gone when you want to draw on it.