Okay, prior to the 12th amendment, this type of issue wouldn’t even have arisen, (I know, the term limit wasn’t put in until the 22nd Amendment - bear with me). That’s because originally, the runner-up in the presidential election became the Veep - see Article II, section 1, paragraph 3 of the U.S. Constitution, which reads:
“In every case, after the choice of the president, the person having the greatest number of votes of the electors shall be the vice-president.”
So, when the Constitution was first adopted, exactly the same rules of eligibility applied to the Veep - implicitly, no person could be elected Veep who could not be elected President.
When the 12th Amendment was passed, changing the rules for the Veep to the current system, they made this rule express. The closing words of the 12th Amendment are: “But no person constitutionally ineligible to the office of the President shall be eligible to that of the Vice-President of the United States.”
I think that the plain meaning of the 12th is that only those who can become President can hold the office of Vice-President. That’s been consistent under both the original provisions, and the 12th Amendment.
The argument of those who say Bill could be Veep turn on the wording of the 22 Amendment, which says, “No person shall be elected to the office of the President more than twice…” They argue that succession from Veep to Prez is not election, and therefore Bill could be Veep.
This argument strikes me as implausible, because I would think the phrase “constitutionally ineligible” in the 12th Amendment would be given a broad interpretation, to reconcile the purpose of the two amendments. Put simply, the 12th says that you have to be able to be President to become Veep. The 22nd says if you’ve already served two terms, you can’t be elected president again.
If you can’t be elected to the presidency, aren’t you “constitutionally ineligible”? I think other interpretations are pretty strained. It would mean that the drafters of the 22nd Amendment wanted to change the principle that the drafters of the original Constitution, and the drafters of the 12th Amendment, both enshrined - that you could only be Vice-President if you could be President. It seems odd that an amendment designed to limit the President’s terms should inadvertently change this basic principle concerning the Veep.
But what do I know? I’m just a Canuck.