Gaku Miyama holds the position of president of the Miyama family, a fifth-generation subgroup operating directly under the Tokusa, the largest yakuza organization in the Kanto Region. He is also the great-uncle of Kirishima Miyama, one of the main characters, though Kirishima refers to him as his grandfather. In his youth, Gaku is said to have borne a strong physical resemblance to Kirishima, possessing an elegant and dignified demeanor that has since given way to a commanding presence in his older age. He has a distinct physical characteristic in the form of a scar located near his left eyebrow, a mark he has had since he was younger.

Personality-wise, Gaku is portrayed as a reserved and calculating individual who exudes the quiet authority expected of a true yakuza leader. He is described as being very strategic and sharp, ensuring his family remains strong and respected through a silent and meticulous form of leadership. Despite his high-ranking position, he is not known to have a wide circle of acquaintances. However, he shares a deep, long-standing friendship with Renji Somei, the leader of the Somei group from Osaka. The two men have been friends since they were young, and it was their shared effort that brought an end to a sixty-year feud between their respective families. Their bond is significant enough that Gaku has a habit of teasing Renji with the nickname Renko-chan.

Gaku's motivations appear to be rooted in maintaining the strength and stability of his organization and the peace that was forged with the Somei group. A key part of this peace agreement involved orchestrating an arranged marriage between his great-nephew, Kirishima, and Renji's granddaughter, Yoshino Somei. His role in the story is primarily as a supporting figure, representing the older generation of yakuza leadership who pull the strings from behind the scenes. He serves as an authority figure to whom Kirishima is beholden and who interacts on equal footing with Renji.

Gaku's key relationships are defined by his dealings with his contemporaries and his complicated connection to his own family. His friendship with Renji Somei is his most notable peer relationship, built on mutual respect and history. Renji is one of the few people who knows that Gaku cannot handle alcohol well and becomes sleepy when he drinks. In contrast, his relationship with his great-nephew Kirishima is markedly distant and neglectful. Gaku is revealed to be a poor caretaker, having provided Kirishima with only a monthly allowance and no further emotional support or guidance, forcing Kirishima to become independent without family affection. He has even physically struck Kirishima for addressing him as Gramps. This neglect is further contextualized by the fact that Gaku is considered the black sheep of his own family, with whom he no longer has contact. Through his interactions with Kirishima, he has allowed his great-nephew to develop in a manner that mirrors his own younger self, as both share similar mannerisms, fighting prowess, and an inability to drink sake.

Regarding his development, there is little indication of personal change or growth within the narrative itself, as Gaku remains a static figure representing the old guard. His history includes being the only person to have ever defeated Renji Somei in either a verbal or physical confrontation, demonstrating his formidable capabilities. His notable abilities lie in his strategic acumen and his capacity for leadership, maintaining the Miyama family's position within the larger Tokusa clan. While not directly shown in extensive action, his fighting ability is implied by his past victory over Renji and is reflected in Kirishima, who is known to be exceptionally skilled in combat.