I have a question for anyone who might be a department chair or on a search committee. What does it mean if you get invited for a second on-campus interview? I have already been there once for a standard on campus interview. For context, this is for a tenure track assistant professor position in the sciences.
I have been a department chair (math department, large US university) and nonetheless find your situation completely baffling. I have literally never heard of a TT job candidate being invited to a second on-campus interview. This is so unusual that I can’t really come up with a plausible guess for why the department that invited you thinks they need you to visit again; moreover, I think this may potentially bring the competence of the people who came up with this plan into question.
Please don’t rely on idle speculation by strangers online. My advice is to email the people who invited you and ask them to clarify what their plan is for the second visit and why they think it is needed. In my opinion, if you already had one on-campus interview, at least in a normal situation they should have all the information about you that they need in order to make a hiring decision. So I’m guessing their explanation may not be the most logical one. But at least you will have a sense of where they’re coming from.
Generally it would mean that they are very interested, but not absolutely sold. It may be that some senior professor wants to see more of you or meet you for the first time. They may want some student opinion in some places. It isn't frivolous, since they are spending some money, but you still have to close the deal.
In the long term it is probably a good sign that if you get the job they are treating you as a serious contender for eventual tenure. They are doing more than just filling a temporary slot.
But, close the deal.