I thought it was Jeff Cooper that advocated strong thumb down underneath below the safety; not Mas Ayoob.
Ayoob does for sure.
Cooper had big hands, and I think, advocated thumb riding the safety. He also deactivated the grip safety, since thumb riding safety prevents the hand from pushing the safety in as far. Today, that problem is alleviated with the modern grip safety with the "bump". I used to shoot thumb on the safety, but Farnum taught us to raise the strong thumb behind it. That pushes the safety plenty far and prevents thumb rash. Sandwich the safety between the two thumbs.