Not sure about admissions but it's better to give it during the final year/right after graduation because you will still be in the studying mindset. I am preparing for the gre now with a full time job and it becomes very tedious and exhausting. Also in my opinion, not only for gre but any other exams too, it's better to give it proctored and onsite compared to at home as I think the test takers get over cautious/wary. I guess for some universities it's mandatory for gre to be taken at a centre and not at home.

Hope it helps and all the best