Kamui's initial appearance is likely a homage to Shishio Makoto of Rurouni Kenshin fame, just one of many references to the series made throughout Gintama.
Kamui is ranked as the biggest eater in the series.
Kamui's hair was actually black in a flashback in Episode 42 of the Gintama anime, and also in an ending before the Yoshiwara in Flames arc. After the ending credits of Episode 146, Ginpachi-sensei read aloud a fan letter about Kamui's black hair, ignored it and threw it in the Rejection Box.
Kagura states that their father, Umibouzu got a shotgun marriage and that he mentioned that love starts in bed, so it might be possible that Kamui was born before their parents got married.
He is the same age and height as Okita Sougo. This similarity might have been intentional as in Lesson 505 the two are revealed to be equally sadistic and appear to form a rivalry. As such, this fact might have been some form of foreshadowing by the author.
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