Take it one logical step further: What Graham has to worry about is when he tells some BS under oath, and the recording shows that is a lie, he can be charged with perjury. And if he just takes the fifth, then his only "testimony" is the recording itself. So this is a perjury trap for him. And even if he has a pocket pardon from Trump, that does not protect him from crimes (like this perjury) that he did after Trump gave him the pardon. Even worse, from Trump's perspective, is if he pulls that pardon out of his butt then he can't plead the fifth for anything before the pardon. He either testifies (truth or perjury) or goes to jail for contempt.

If he wants to save his ass, his best play is to flip on Trump and get immunity in exchange for testimony about EVERYTHING. And immunity deals do require the witness to testify about everything the prosecutor cares to ask. Of course, maybe he's looking forward to some enjoyable times with cellmate buddies in prison.

Educating anyone benefits everyone.