Aki’s neighbour event starts automatically after day 50.
For several mornings, the protagonist wakes up because of renovation noise from next door. Keep sleeping until he decides to go outside and investigate. There he meets Aki, the new neighbour, and notices a hole in the wall between the properties.
Continue sleeping through the following mornings to advance the event. A few days later, go outside when the next scene triggers and you will see Aki talking with Naruto through the hole.
The remaining Aki scenes continue through the same morning-at-home event chain. No special items are required; if the next scene does not appear immediately, sleep until another morning.