A bureaucrat at an agency outside time who spends four hundred years filing cases and has never once been asked whether he chose the job.
Owen Wilson playing a middle manager at the end of time is the joke, and it works because he plays it entirely straight. Mobius investigates dangerous variants, believes the paperwork, and is kind to a god of mischief for long enough that the god notices.
What the second season does with him is quietly cruel: he has been at the TVA for at least four centuries, he has been mind-wiped repeatedly, and he had a life before it. He was Don, who sold jet skis in Cleveland and had two sons. Being told that does not undo four hundred years, and the series knows it.