You pretty much have to talk to Akinari first, you should have seen him in one of the Hanged Man S. Links, Maiko informing you that he only shows up in the Shrine at Sundays. Once you talk to him he'll tell you of a fountain pen he had lost, that being what is needed to start the S. Link. Once you've learned about the missing pen, check Koromaru at night (he sits next to the TV at the dorm. You'll get the pen back. Do it by 9/6 or you may miss the Sun social link.