Nagai serves as a police officer, identifiable by his dark hair and mid-dark eyes, consistently clad in a standard police uniform during duty. His core narrative role centers on surveilling Tatsu, the former yakuza dubbed "The Immortal Dragon," driven by deep-seated caution over Tatsu's criminal past. Nagai possesses intimate knowledge of Tatsu's exploits, including the legend that Tatsu "singlehandedly smashed up 10 of his rival clan's offices in one night, completely unarmed." This awareness fuels Nagai's persistent suspicion that Tatsu remains engaged in illicit activities.

Their interactions typically occur during Nagai's routine patrols or investigations, often intersecting with Tatsu's domestic tasks or errands. These encounters emphasize the contrast between Tatsu's current civilian life and his formidable reputation, with Nagai interpreting mundane household actions through the lens of potential criminal behavior.

No significant character development or expanded backstory beyond his professional role and cautious demeanor toward Tatsu is detailed. His surname, meaning "eternal" (永) combined with "well, mine shaft, pit" (井), holds no direct narrative significance within the sourced material.