Here's the tiny mention in there:

Chuck Rosenberg:

No, you’re referring to Section 3 of the 14th Amendment. It’s not self-executing. I’m not sure what the triggering mechanism would be, and I agree with you. It ain’t going to happen. Interesting intellectual exercise. It sounds a lot like my three years in law school. If you look at my transcript, you would see it didn’t go that well.

Except that it very clearly is self-executing. I'll paste it in here again for easy reference:

Section 3 Disqualification from Holding Office

No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.

Breaking it down:

What is the disqualification from office stated in the section title? "No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, ..."

Who does this apply to? Anyone "who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof."

What is the remediation for this disqualification? "Congress may by a vote of two-thirds of each House, remove such disability."

As a comparison, Article II, Section 1, Clause 5 reads:

No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.

If a 23 year old Frenchman decided to run for US President, what would happen? Would there need to be some kind of trial or judicial review? No - state officials would disqualify Mr. Young French from appearing on the ballot. And then, if Mr. Young French wanted to protest that decision, he would initiate a court filing, after having been disqualified.

14A S3 is self-executing. The reason Rosenberg in the podcast says he's "not sure what the triggering mechanism would be" is because there isn't one.