you shouldnt be seeing patients, unless you had student affairs extend your malpractice insurance to the 2nd look institution to cover you in case something happened. you may shadow attendings/residents at some places, however....that is institution dependent.
i have had 2nd look students just come hang out with the residents, get to know people, talk with attendings, hang out in dosimetry, go to a tumor board, and attend dept conferences....pretty laid back. dress nicely (shirt and tie is ok). i dont think there is a need for your white coat...