Just for information, I heard about the time there was a problem with someone being Speaker and Lieutenant Governor. After that time there was an amendment (Improving the chain of command amendment) accepted by the population in July 2013.
https://uselectionatlas.org/FORUM/index.php?topic=176511.msg3801017#msg3801017I think it was in part to solve the problem of the same person holding the two office. If the person disappear, the power of speaker goes to the most senior representative in terms of length.
Not sure if it was modified after it was adopted. It doesn't specify who runs the booth for speaker nomination.