My xh use to do that here, as well as at my parents. He would also come to the house when I wasn't home, come into the house and I guess either sat around or slept. I deliberately stopped dusting because I wanted to see what he was doing. It was very strange, but to this day, I don't know what he was doing. I had a password lock on my computer and had the TV's on certain channels, etc. so that I could at least have a sense of what he was doing...but no...I'll never know.
They really do some strange stuff and there's no rationale for it.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.