My friend's cousin's uncle's wife's husband's dad's son's nephew's uncle's nephew's friend just informed me the cut area was actually a lake with a small island in the middle with an old man standing on it. After the nighttime transition sequence on the 16th of any in-game month, the player will have to enter the area (named "Shijūkara") within five seconds in order to activate the side quest. As soon as the player steps foot at the edge of the lake, Ryo receives a notebook entry which reads, "Dreary desolate. A normal, old tissue prowls because of the wife."
It is not self-explanatory in the very least, but the player is required to talk to the woman in Tomato Convenience Store and fill in the gaps of the haiku in a similar fashion to Master Chen's password system. Upon doing so, she will mumble and point downwards. The player must then buy five portions of Sliced Fish and head to the Yamanose shrine. Once the dog in the distance has barked on three occasions, it is time to feed the Sliced Fish to the kitten. After feeding the kitten the fifth portion, it will let out a freakishly long meow. Ryo's attention will be drawn to the offerings board at the shrine and the interaction ends.
The player will find a Mahjong tile sitting on the offerings board, which must be picked up to continue with the side quest. The next destination is obvious: Daisangen Mahjong Parlour. The player must stand in front of the owner, open the inventory, and use the tile. This will lead to "..." being displayed as a subtitle for ten seconds as the owner stares at Ryo with his characteristic soulless look. At some point within that ten-second window, a QTE prompt of A, B, or X will suddenly flash up. If the player succeeds, Ryo will duck, spin, and land an absolute cracker of a punch to Dick Phillips' guts. If the player fails, Dick smashes a bottle over the back of Ryo's head, the screen will turn black, and Ryo will be standing at the phonebox in Sakuragaoka, locked out of Shijūkara for the rest of the playthrough.
With Dick down, Ryo will search through Dick's pocket and pull out an item named "Tongue." The item is nowhere to be found in the inventory, but the image accompanying the pop-up when Ryo acquires the item appears to be a sack of something. At this point, the quest is essentially complete. Returning to Shijūkara, a narrow wooden bridge connecting the land to the little island has since appeared, thereby allowing Ryo to reach the old man.
After making it across the bridge and interacting with the old man - who does not even open his eyes, let alone talk - Ryo will be rewarded with a Poké Ball containing Flareth. Regardless of the time, Ryo's wristwatch alarm will go off and he will head home, at which point it will be 11:30pm.
Hope that cleared things up.