I'm not certain, but before the 12th Amendment, every Elector had two votes. The could cast both for one candidate.
In the Constitution it says in Article II, Section 1, Clause 3 (since superceded):
The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves.
I would interpret this to mean that an elector could not have voted for the same person twice. I would interpret this to mean that an electorwas required to vote for two distinct persons. They were required to do so.
The question that's open to interpretation is whether they are still required now.
There's no language in the XIIth Amendment to supersede this.
Well, it does say he's elected for a four year term, together with the president.
It also does say that if both offices are vacant, and Congress has appointed somebody else to fill their powers, he remains in office until the Electors have voted again (superseded by the XXVth)...this might be interpreted to mean that the term would have ended early, or at least that Congress had the right to legislate that such terms ended early...of course it never happened so it's entirely scientific.