[DoodleDawg]

Can someone appoint him as VP (subject to approval by congress) if the elected VP should resign or die? Yes.

He can't be elected vice-president but he can be appointed to it? By that logic then someone who is 25 years old can't be elected vice-president but could be appointed vice-president.

[SmokingJoe]

It comes down to how the 22nd and the 12th are worded.
If anything like that should happen, it’s going to end up at the US Supreme Court. They can decide.

[Jim Noble]

By that logic then someone who is 25 years old can't be elected vice-president but could be appointed vice-president.

Two different things.

Someone who is 25 is INELIGIBLE to the office of President, and therefore is also INELIGIBLE to the office of Vice President.

But the XXII Amendment does not make anyone ineligible to anything.

What it tries to do is to read 1944 Electoral College appointment practices into the Constitution.

The Constitution doesn't say anything about "running". It also doesn't say anything about political parties, primaries, nominations, conventions, being on the ballot or even the existence of ballots, Presidential elections (except for the electoral college, about which it says a lot). It says nothing about "calling states". It says nothing about "conceding" or "claiming victory".

All of those things are outside of the Constitutional process, are unnecessary for choice of a President, and do not bear on the XII Amendment's criteria of eligibility.