He appears to have some form of friendship with Onoda, wherein he considers himself to be something akin to a mentor figure, but this is more than likely a delusion that he struggles to keep up for himself, especially when Onoda blew past him on the climb in the First Year Welcome Race. He later comes to admire Onoda, which is part of what encourages him to train harder.
His greater experience meant he was able to give Onoda useful tips and practical information about road racing when he had just got into the sport, such as informing him about energy jelly drinks, of which Onoda is always greatly appreciative.
Second Year Events
After becoming a second-year, Sugimoto asks Imaizumi to help him as he trains with the goal of making it to the Inter High. After seeing that Sugimoto is serious, Imaizumi accepts the role of a mentor. Imaizumi actually begins to be quite supportive of Sugimoto, who is deeply grateful for this as he has a lot of admiration for Imaizumi.
During the first year welcome race, Sugimoto imagines his participation in the Inter High as Imaizumi's assist, so it is clear just how much he looks up to Imaizumi. Though Sugimoto does not earn a spot on the Inter High team, he is able to ride alongside Imaizumi before the race begins. He tells Imaizumi that it is an "honor" to be able to ride with him before such an important time. He is even able to pat Imaizumi on the back as encouragement like he dreamed of doing, though not before the goal line as he truly wished. Imaizumi jokes that Sugimoto hurt him, something a bit rare for him, before telling Sugimoto to leave it to him.
Before training camp started, Sugimoto paired up with Teshima in a race around the school, starting from the front gate going downhill, around the streets, then back up the climb up to the back gate. Sugimoto did not consider him to be a fast cyclist on looks alone, but was beaten by him by a considerable margin.
Second Year Events
It is later revealed that Terufumi has a little brother, Sadatoki, who looks up to him. Sadatoki copies everything he knows from his brother, disregarding how different their bodies are and how what works for Terufumi won't necessarily work for himself. His brother's admiration of him helps motivate Sugimoto to get better in his second year.