There are three ways to become vice president
Way one: Election by the Electors
Way two: Election by the Senate (not House)
Way three: Selection to fill a vacancy during the term
Way two is obviously not accessible for Bill Clinton, everybody here has agreed to that.
That way one might be accessible is an absurd proposition: What if Bill and Ronald Reagan are the Dem and Rep candidates, the election goes to the Senate, and the Senators can only vote for the top two vote-getters but not for either of them?
That leaves way three though, I'd have to read the applicable amendments closely; I guess I'll do just that. It would be the intention of those 1960s amenders we'd have to look into here, not that of the 1800s amenders...
And just because somwbody writes a legal paper don't mean anything at all. You'd need to show me a court decision.
It gets even worse:
It could be argued that Clinton might be appointed to fill a vacancy in the Vice Presidency, but could not become president again anyways...