Separately elected Vice President

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Between 1945 and 1964, Brazil's Vice President, who carried the same powers as the US VP, was elected in an election separate from that for President. Usually, the presidential candidate usually had a running-mate but it was unofficial since nothing held a voter to vote for the presidential candidate AND his chosen running-mate, some presidential candidates didn't have running mates and some VP candidates had no presidential candidate attached to the.

So, what if the US Vice President was elected in an election totally separate from President, but on the same day.

What would recent elections look like, assuming the OTL running mates do run in this new setup.