What things can I do as a job market candidate to gauge the internal political culture of a department that is hiring?
One measure of the politics within a department is the faculty member's attitude towards collaborations. When I was touring grad schools as a prospective PhD student I remember interviewing with a faculty member. I asked her if she collaborated with other faculty within the department or other departments. She answered dismissively and instead asked me why I was interested in asking such questions and why it mattered whether she was involved in collaborations. If you get such a response, or sense such attitudes, this might imply there is an unhealthy dose of hostility or competition between faculty within the department.