Found SHIMANEKKO! Trophy

After you've cleared the game once, this sidequest will be available to you. It is one of the three sidequests required to unlock all the gallery entries, and the only one required for the .

It's best to do this during the “Crossing Paths” playthrough, as that seems to be the most consistent trigger of the event. Once you reach Chapter 8 of that playthrough, head to Kamiari-an immediately after leaving the inn. You will be greeted by a man looking for SHIMANEKKO. Check the sign outside Kamiari-an to get the quest started – you'll see SHIMANEKKO and he'll run away.

The steps you need to take, in order, are:

Kamiari-an: Check sign
Shimane Art Museum: Go inside
Vacant Lot: Check white house
Shimane Art Museum: Go inside
Matsue Station: Check road
Shimane Art Museum: Go inside
Kyomise Shopping Area: Check red mailbox
Shimane Art Museum: Go inside
Shiroyama Park: Tourist Information Center (not inside) – Check vending machine
Shimane Art Museum: Go inside
Matsue Oba High School: Field – Check field
Shimane Art Museum: Go inside
Shiroyama Park: Matsue Castle – Check path
Shimane Art Museum: Go inside
Usagi Theater Company: Inside – Check right window with mopeds
Shimane Art Museum: Go inside
KARAKORO Studio: Check right desk
Shimane Art Museum: Go inside
Shiroyama Park: North Soumon Bridge – Check bridge

Alternately, during “Crossing Paths”, you can trigger this sidequest during Chapter 9 (“Rain Stationery”) after checking out the used bookstore.