It comes down to a determination as to what the term "eligible" or "eligibility" means. Does it mean "capacity to be elected" as posited by Eugene Volokh (entry of 3/8/2004 03:23:40 PM)? Or is there a distinction between the terms "election" and "service"? See Bruce G. Peabody, Scott E. Gant, Twice and Future President: Constitutional Interstices and the Twenty-second Amendment, 83 Minn. L. Rev. 565(1999).
As I stated before, I think it is an open question, and not one where it can be stated as a flat assertion that it would violate the Twenty-Second Amendment (as incorporated into the Twelfth Amendment) for a formerly twice-elected President to serve as Vice-President.
He has to hold office in the line-of-succession to be eligible. He does not hold such office, therefore he is ineligible.
It is simple, and it it is meant to be simple. But lawyerese always leaves an opportunity for "nuance" (feh) when the lawyers don't intend to.
Why, oh WHY, couldn't have said: "If you have been President twice, then you can't be President again or Vice President."