This happened often enough, and his lawyer always advised him to not say a word, but especially when he'd been drinking, the act of getting him to talk long enough to say that he was invoking his right to silence would usually reveal that he'd been drinking.
To mitigate it, he printed a laminate card, that he kept in his wallet, which very respectfully and politely invoked his right to silence. When pulled over, he would simply remove the card from his wallet and hand it to the officer.
I don't know that it ever got him into or out of any trouble, but at least he had a routine, and it prevented him from talking unnecessarily.
Perhaps the author could have made use of something like this?
In the real world behavior like that causes police to treat "refusal to talk" as "guilty". Stories like this post are very far from the norm.