What is the mechanism behind that? All that springs to mind as a theory would be lagging effects of testosterone surges.

I believe it's a joint effect of muscle atrophy (vocal folds lose mass and become thinner), lower testosterone levels, stiffening of the larynx and the general loss of elasticity (stiffer things vibrate with a higher frequency). I'm no expert, though.

To be clear, we're talking about 60+. Before that, the pitch usually is on a decline.

In his case, quitting smoking, I think.