This amendment does imply that someone could run as vice-president. The whole paired “running mate” thing is not enumerated in the constitution as far as I know.
Typically, the popular vote has the two tied together, so that in many states the Pres and VP get the same popular vote and the electors go for the pair.
Imagine someone running as VP as an independent and getting more EC votes than one of the paired “running mates”!
Interesting - so what if independent conservatives put-forth a conservative nominee as VP?
If we did not like our GOP presidential nominee we could by chance force someon in the VP slot. . . .?