Replying to both 384 and 386.
Post 386 first: You are correct the rule refers to both president and vice president however, it refers to demonstration of support prior to name being placed in nomination for the office in question, not prior to the convention. Being he was the selection of the presidential nominee, I doubt there was any difficulty in receiving statement of support from a majority of delegates in 8 states.
Post 384: I probably did not express myself clearly enough but it is not rule 40(b) and the 8 state requirement that would prohibit Mr. Ryan or anyone else for that matter, from being entered in nomination after the first ballot. Rule 40(e) controls what happens after balloting starts. It specifies clearly that if no one receives a majority on the first ballot, the next step is for the chairman to call for a second ballot and then a third, forth and subsequent ballots until a majority is reached. It does not provide for going back and reopening the nomination stage, only for continuing to vote until a majority is gained. It is somewhat like a state primary where there is a cut-off date for getting on the ballot. After that date if someone has not qualified for the ballot, they are not allowed to get on the ballot after voting has started.