[angkor]

Because he's still Constitutionally eligible to BECOME President, he's still Constitutionally eligible to RUN FOR Vice President.

You're getting caught-up in bizarre semantic thickets.

Ineligible means can't run, can't assume, can't hold.

He cannot hold the office again (nor that of VP), because the Constitution says one cannot hold more than two terms in the office.

What are you missing?

[Iota]

I'm not missing anything. Read the Constitution itself. The 22nd Amendment says, and I quote: "No person shall be elected to the office of the President more than twice". You seem to think it says "No person shall BE President more than twice" or "No person shall SERVE MORE THAN TWO TERMS AS President." But it doesn't say that. It says what it says. And, because it says what it says, it bars two living Americans from running for President. But it does not bar those two Americans from becoming President via the Vice Presidency, or via the office of President Pro Tempore of the Senate (4th in line of succession) or via the office of Secretary of Veterans Affairs (17th in line of succession). All it says is you can't be elected to the Presidency more than twice.

Think of it this way: Back in the late 1940s and early 1950s, when this Amendment was being debated, people weren't worried about some popular politico Grover Clevelanding his way in and out and in and out of the presidency (a la Winston Churchill and the Prime Ministership). In other words, they weren't morally outraged at or mortally offended by the prospect of someone simply serving as president for more than eight years. Instead, they were worried about an FDR-like creature using the power of the presidency to see himself reelected indefinitely, becoming a de facto dictator. Thus, they put a limit on the number of times someone could be ELECTED president, not how many times someone could SERVE as president. If the president makes it in for a third term via the vice presidency or the Speakership, for example, he wouldn't have done so via the FDR route, which is what they were trying to avoid.

[Izzy Dunne]

Constitution says one cannot hold more than two terms in the office

Sorry, but that's not the case. Without much doubt, a person could serve 10 years - 1 day, right?

From the 22nd Amendment:
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once.

So, he cannot be ELECTED again.
Does that mean he is not "eligible to the office" ?
As much as you or I don't like it, It's a debatable question.