A few people have pointed out to me, thanks to their mad wikipedia skills, that the term gerontocracy already exists and describes a form of governance similar to this thing that I posit.
Gerontocracy existed in Russia during the Cold War. It was a way of explaining that though their leaders aged, they never left their positions in the Communist hierarchy. The system was a static one created by late-middle-aged politicians, much like the ones that rule...everywhere, even here. They were not chosen for their age, their life experience, their values. They just had the right connections and toed a party line.
What I purpose differs in that aging into a position from an unappealingly youthful age (under 70) would be nearly impossible. Those who rule in a geritocracy would already have some serious seasoning before they even got to be so much as dog-catcher. It's not an aging system (much). It's a system run by the aged. No networking. No partisan politics.
And that's different.