Have you looked into Saito Past? Like how he joined the Shinsengumi and the reason he is the way he is? Better understanding is from watching Hakuoki Reimeiroko.
That being said, You have to understand that Saito is a strong willed person who has over come so many hardships in life. One of the few with a warriors spirit which is why he chose to fight beside Hijikata.
To fight for honor means everything to a samurai. To die an honorable death is the greatest thing one can achieve.
I hope this made sense D: Im the worse when it come to putting my explanations into words for others.