I would expect that that the mod that is not on rotation should not be doing mod work like banning users etc. if there are issues with mods switching to anonymous accounts and not being banned, when the mod moved off rotation, the post can still be reported and a more objective mod will review the post/user.
if every time the anonymous user is banned and the problem mod rotates in and unbans a user, we would be able to identify the problem mod after a few unbanning