Well, there are lots of hints about Tyrion being a Targaryen bastard.
So, Aerys raped (or maybe it was not a rape) Joanna. A man like Tywin would never suffer such an insult as a living bastard Targaryen child that soiled his marriage and killed his wife. So why Tyrion is alive? Tywin hated him, abused him, humiliated him and disinherit him. So do we have another dying wish, that goes like this: "Promise me.. Promise me ... Tywin..."
Just a thought.