Ichiko is, in fact, a ghost. Her story begins 22 years ago: a previous Elder (actually Mizuho's mother) had a close relationship with an underclassmen who had a weak body. When that underclassman heard that the elder was graduating and getting married the same time, she had to see her before she left. The underclassman went to the Elder's room, and waited, but she died before she had the chance to talk with the Elder. That room has been deemed the "closed room" ever since, until Mizuho arrived and started living it, according to his grandfather's will.
She is very energetic and hyperactive, often talking very fast. She took some time to understand that she is a ghost, and by that, dead. She says that Mizuho looks very much like her previous Elder love interest.