All jokes aside, I'd say there's a good chance he'll stick nearby or even come back to the same ridge or drainage.
As an example- in 2021 on my cousin's LE hunt in the Book Cliffs, we had seen two mature bucks together on three different days. On my cousin's last day, he took the older, better buck while his buddy was feeding about 60 yards away (as well as several does). Upon shooting his buck, the buddy buck continued to feed until we got out to his dead buck to clean it. Then he moved into the cedars... Once we got the dead buck dragged out of there, we turned back, and the buddy buck was back out feeding in the same spot. Probably happy his older brother was gone for the rut...