Thanks, but would't you say that para. is just about election in the house and not general election?
No, I wouldn't say. The house cannot elect veeps at all. The senate can only choose between the two people who received the highest total of EVs for VP, so such an interpretation makes not a single bit of sense.
Basically, it seems they just forgot to start a new para for that last sentence.
Remember: Before the XII amendment each elector had two votes that both were for VP and prez, so it was obvious that only persons eligible as Prez were eligible as VP. If that last sentence of the XII weren't there, that would have been accidentally repealed. (Note that these requirements at the time did not include a term limit. They were actually talking about 35 years old, native born or immigrated before 1776, US citizen, that kind of thing)