Nekomata/Carroll in Wonderland

The Nekomata (帽子屋さん Bōshiyasan) is a minor character in Carroll in Wonderland.

Timeline
In general, Nekomata can be found in Castle Gate each day, accompanied by the Hatter.

Day 1
Nekomata is in Castle Gate from 10:00 to 19:00. If the player talks to Diamond Soldier (in the Entrance from 12:00 to 21:59) and picks "Talk", then "Chat", then she will mention how Nekomata is playing around with a keychain. From this point, Nekomata will have lost her Fish Keychain. This item can be found by talking to the sleeping Succubus NPC who's facing the wall in Castle Gate.

Day 2
Nekomata is in Castle Gate from 10:00 to 14:00. If talked to during this time, she will move to the Great Hall and distract the guards here, allowing the player to examine the door to the Queen of Hearts' room (thus eavesdropping on a conversation).

Day 3
Nekomata is in Castle Gate from 14:00 to 17:29.

Presents
The Fish Keychain can be given to her and causes her to give you the Hardwood in return.