There is a trick to it. Just ask the same question over and over again without acknowledging his non answers. Especially around a group of people like family members. What that gets across to everyone is that he didn’t answer the question because he doesn’t know the answer, or worse, is unwilling to answer it. If he does answer it, focus on the answer and ask the next obvious question that he will not answer. Essentially an adult’s way of the little kid that keeps asking “why” to everything he hears.
My wife’s uncle was the same way with the entire family. As he was a union shill, it was easy for me to tear his biases apart. It really pissed him off so badly that he never came around again while we were visiting the area. Family members in later visits thanked me for what I did. They were used to being bullied by him and his ego soaked up the unwillingness of them to challenge him.