This is another one of those lovely “true 100% of the time” rules — they pop up so infrequently on the SAT that you really do appreciate them when they appear. Even better, this is a rule that the College Board tests pretty often, so there’s a decent chance you’ll come across it in any given Error-ID section. And if you do happen to encounter it, it’s an easy point. You don’t even have to think about the other options. Here’s why: “Between” is a preposition, and prepositions are always followed by object (rather than subject) pronouns.
Since the “you” forms are identical in subject and object form, SAT does not test them. Most often, it tests the first person singular (I vs. Me) or third person singular (he vs. him).
Subject pronouns are used as subjects, while object pronouns can be used as objects (I know, big shock there).
To give an obvious example, you would say, “I went to the store,” not “me went to the store” because “I” is a subject pronoun; however, you would say “I see her,” not “I see she” because “her” is an object pronoun.
Likewise, you’d say “This book is for her,” not “This book is for she.” Thus, you would always say “between you and me” (preposition + object pronoun + object) pronoun, NOT “between you and I” (preposition + object pronoun + subject pronoun).