Burke is the founder of modern conservatism. He established the pose. Buckley is a well-known intellectual conservative. Carlson stands in for Fox News, and Fox News is indeed a thought leader for American conservatives. I don't go into Carlson's views in much depth here, but just point out the low standards for intellectualism in American conservative circles (because Trumpism is obviously populist and anti-intellectual).
Also, this article is just one in a series. Much more is on the way, including articles on Jordan Peterson, George Wills, and possibly Julius Evola.
Who would you say are the top intellectual conservatives?