Yamaguchi and Ishigaki are good friends, as the flashback to pre-Midousuji Kyoto Fushimi exemplifies. Yamaguchi called out to Ishigaki when he was left behind on the second day of the previous Inter High and Ishigaki seemed distressed about the decision to abandon Yamaguchi and Ihara.
Second Year Events
Ishigaki spoke to Yamaguchi about the Inter High on the day of his graduation from high school. Ishigaki praised Yamaguchi's performance in the previous Inter High and asked Yamaguchi to act as Midousuji's "conscience" in the next Inter High. Essentially, this means that Yamaguchi should stop Midousuji if he goes too far. Even though he lacks confidence and questions his capabilities, it appears that Yamaguchi wants to accept the role Ishigaki entrusted to him.