Pupillometry has been used to assess effort in a variety of listening experiments. However, measuring listening effort during conversational interaction remains difficult as it requires a complex overlap of attention and effort directed to both listening and speech planning. This work introduces a method for measuring how the pupil responds consistently to turn-taking over the course of an entire conversation. Pupillary temporal response functions to the so-called conversational state changes are derived and analyzed for consistent differences that exist across people and acoustic environmental conditions. Additional considerations are made to account for changes in the pupil response that could be attributed to eye-gaze behavior. Our findings, based on data collected from 12 normal-hearing pairs of talkers, reveal that the pupil does respond in a time-synchronous manner to turn-taking. Preliminary interpretation suggests that these variations correspond to our expectations around effort direction in conversation.