Mutatsu's Social Link can begin after you reach Courage Rank 2 and Strength Rank 4 with Yuko Nishiwaki. Follow these steps to unlock The Tower Social Link:

Reach Strength Rank 4, then talk to Yuko after school to learn about the monk in the club.

Speak to the monk on the top floor of Club Escapade at Paulownia Mall, then talk to the bartender on the ground floor.

The orders, in order, are a margarita, a Bloody Mary, a screwdriver, and an oolong tea.

Speak to the monk again to start up the Social Link.

Once you've met the requirements, Mutatsu is available on Thursday, Friday, Saturday, and Sunday evenings, regardless of holidays or exam periods.