Isn't teaching part of the definition of faculty? In other words, isn't it impossible to be 'faculty' if you don't take 'students' (i.e., 'teach')? At least anywhere I've ever heard of, this is true; someone who doesn't have students is considered 'staff'.
> Isn't teaching part of the definition of faculty?
No - I'm not sure where you got that definition from. You can be a researcher and be on the faculty of a department. It just means as opposed to the support members of staff.
I'm guessing you're either tenured or emeritus, or you're a research professor. You don't have that luxury on tenure track almost anywhere.
TT faculty at SLACs don't take graduate students (by and large) and still get tenure...