The "proper piece" for dealing with red-eyed enemies; found in a campfire in Hirata Estate .

Are you trying to find a specific item to progress past a certain boss? Sekiro: Shadows Die Twice - Walkthrough Part 1: Shinobi

If you are looking for a "piece" to complete a larger set, it's likely one of the three fragments of the Dancing Dragon Mask :

Sold by Pot Noble Kormori at Fountainhead Palace for 12 Treasure Carp Scales.

Sold by the Dungeon Memorial Mob near the Abandoned Dungeon Entrance for 5,000 Sen. 2. Key Prosthetic "Pieces" (Early Game)

Essential for stunning beasts; bought from the Crow's Bed Memorial Mob for 500 Sen.

Sold by the Pot Noble Harunaga in Hirata Estate for 7 Treasure Carp Scales.