In older builds, Student-kun existed as a placeholder for Senpai. He never reacted to anything happening around him, making him not very important.
His purpose was to be Senpai, of course. You can't be a yandere without having someone to kill for.
He was seen in one of YandereDev's videos. In it, he spends all time talking to a yellow-haired Student-chan. Due to her not having blue hair like the other Student-chans, she was nicknamed Goldie-chan. His only other known appearance was in YandereDev's first video, in which Ayano Aishi sees a Student-chan talking to Student-kun in a classroom, so Ayano runs into the room to beat up Student-chan.
Taichi Hayami is the name of the default male student model in Yandere Simulator, which was used to represent Student-kun and later recolored in later builds to create Senpai's model. He is the base model for every male student in the game.