I didn’t realize the whole House participated in the second vote. I didn’t bother to look it up, but that even concerned me about the first vote, not realizing only the Republicans could participate.
The second round of voting is mentioned in this article with no restrictions...a second round would mean all not part.
http://www.politico.com/story/2015/01/john-boehner-house-speaker-vote-113992.html
I would not think only a few would re vote, therefore with chaos, it would be possible for a really split vote if Boehner lost first time...opening a door for the Wicked Witch of the West. So be careful what you wish for, and if anyone can find anything different please post it.