A friend brought it up and I told him that I'd look into it.
I know that the amendment does not define the term limit as “eight years” or “ten years.” It speaks of “terms.” No one is permitted, after being elected to and serving two terms as POTUS, to be elected again, or to serve any additional time as POTUS. Thus, no one who has served eight years as POTUS is allowed to be elected VP, because the qualifications for VP are identical to those for President.
Suppose a one-term President ran for VP. He would be eligible to serve another four-year term if the President dropped dead on Inauguration Day. Or, he could serve less than half of someone else’s term, and run for one more term of his own.