Kyūju Amagiri (天霧九寿, Amagiri Kyuuju) is a demon serving the Satsuma Domain. He has definitive red hair, cyan eyes, and a goatee. He is an honorable man who treats everyone with equal respect.
Amagiri is a fictional character and does not have a historical prototype. He always follows Kazama and serves as his voice of sanity when it is time to stop fighting and leave in order to either not bring shame on Satsuma's name or not stray from the Demon's Path.
Appearance
Amagiri is a tall and bulky middle-aged man. His distinguishable feature is his long red hair that he wears in a ponytail behind, and his bright cyan eyes. He is always seen wearing traditional clothing (dark-purple trousers and red-vine top) with a black haori and long gloves. The pattern on his haori's shoulders is a white snake forming the infinity symbol ∞.
Personality
Kyuujyu Amagiri is a very strong and mature oni, who prefers to fight with his fists instead of a sword. He is usually seen by Kazama's side as his companion and advisor but they both seem to work for the Satsuma Domain. Amagiri is very polite towards everyone, whether friend or foe, he is able to apologize when he is wrong (or when his subordinates are wrong) and express gratitude when it is deserved. For instance, he acknowledges Hajime Saitou's power and thanks him for choosing to solve the conflict with words. He always bows to his enemies when he leaves, as a sign of respect.
Amagiri seems to dislike fighting and often asks his opponents to avoid it. He never taunts his enemies and never drags them into fight forcefully (unlike Kazama). When he has no choice but to engage into a battle, he strikes once and hopes that the damage dealt is enough for the opponent to stop.
Despite being powerful and apparently an important figure in the demon world, Amagiri is quite emotionless, he is never seen screaming or getting angry or even changing his facial expression from indifference to any other emotion.
Story
First Season
Amagiri always accompanies Kazama except for the scene where he meets Saitou for the first time while his (apparently) subordinates are taunting and insulting the Aizu and the Shinsengumi.
He is first seen at Ikedaya along with Kazama while watching the Shinsengumi raiding the inn and fighting the Chōshū. When challenged by Heisuke, Amagiri asks him to reconsider fighting, but since Heisuke insists, Amagiri knocks him out very quickly.

SatChō and the demons attacking Sano and Shinpachi
His further appearances, excluding the one when he met Saitou, are quite minor. They are mostly him scolding Kazama for recklessness or assisting him in his attempts to kidnap Chizuru. However, one of the notable ones is his involvement into the ambush that the SatChō have prepared for the Shinsengumi after the latter have killed Itou. When the battle seems hopeless for the Shinsengumi, Amagiri suggests that Sano and Shinpachi give the demons Chizuru in exchange for their lives being spared. They refuse, and Heisuke joins the fight striving to take revenge for his previous lose against Amagiri at Ikedaya. However, Amagiri hits him too hard, and Heisuke ends up gravely wounded (and becomes Rasetsu to survive).
Amagiri's last appearance is in the season finale when he stops the battle between Kazama and Hijikata (with Yamazaki's assisting sacrifice) and urges the demon to retreat.
Second Season
In the second season of the anime, Kazama, Amagiri, and Shiranui are united against Koudou and his daytime Rasetsu.
At some point, Amagiri reveals to Saitou that the Rasetsu are slowly wasting their lives away by using their powers, because the power of Rasetsu is not magic but overuse of their inner life force. He also advises him to warn the other Shinsengumi who have drunk Ochimizu.
Later in the season, Amagiri witnesses another battle between Kazama and Hijikata and reminds the former that he warned him not to become emotionally involved with the human. He also informs him that continuing the battle will result in Kazama becoming an outcast and not part of the demon society, but when Kazama dismisses the comment angrily, Amagiri steps back. When the battle is forced to pause because of the fire, Amagiri claims that Hijikata can do whatever he pleases about Kazama as the demon is not his concern any longer.
Sweet School Life
In the short OVA, Amagiri is shown very briefly as a student at Hakuou Academy. He and Shiranui appear by Kazama's side when Kazama walks onto the stage to make an announcement as the President of the Student's Council.