> First, all you need to do is shut up to exercise the right.

Actually, as I understand it, SCOTUS has said that merely being silent is not the same as invoking your Fifth Amendment right to remain silent. I think this jurisprudence is complete bananapants, but the argument is that you have to explicitly and unambiguously invoke your Fifth Amendment right for it to kick in, and being silent isn't an unambiguous invocation.