If elected which party would you caucus with? This could be of particular importance if both Labor and the Federalist party gets 4 seats each.
As the speakership is no longer a partisan office, I don't think this would have any great impact on how the House operates — so long as Thumb is able to remind himself to vote.
Even when the speaker was still chosen by the caucus system, I don't think Siren or EarlAW ever officially joined a party caucus (though both were, of course, generally left-of-center in terms of voting records).