In the manga, the duration of Gojo's seal is not clearly defined. It's left somewhat open-ended, allowing readers to interpret it based on the context and events that follow.
Jaune could also become angry and frustrated. He might feel that the system is unfair and that he's being wrongly punished. So he could lash out at those he believes are responsible for his expulsion, whether it's a fellow student who set him up or a teacher who didn't give him a fair hearing. In some cases, he may even try to expose the wrongdoings or secrets of the school as revenge for his expulsion.