Are there any "tells" for faculty hires?
Positive early signs:


you helped write the job specification;
one or more of the selection panel advised you to apply for the vacancy;
they take up your references;
you hear through the grapevine that members of your target department have been asking around, about you, after your interview;
you get an additional interview, where the main topics of discussion are pay &amp; other benefits, when you could start, and what facilities you'd require in post.


Regarding formal paperwork,: all applicants at our place are required to show eligibility for employment, at time of interview. So there's no additional requests for paperwork between final interview and job offer.