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In, "they give me the shivers", they is singular.

You did see that I made a distinction between grammatically and semantically, right?

Grammatically, the "they" is clearly plural, as it is used with the plural verb form "give" and not the singular "gives".

Look up "subject verb agreement".

"they" and "you" act exactly the same way. Which is no surprise, because both are originally plural. What difference are you referring to?