Similar to Starfish - I look out a huge window with many panes in it, and look for symmetry in the branches, analyze which window pane capture the best image, and so forth. The window is just to the right of T, so I feel like I'm almost looking at him, just...not!
I also intently study the Persian rug on the floor or the arrangement of items on the table in front of me, and check floorboards and ceiling trim for spiders. More than once I've alerted him to a new web in a corner, occasionally with a resident, and he's always gotten up immediately to get rid of it for me.
Also, he often sits with his legs stretched out in front of him, in which case I'll study the bottoms of his shoes and how his socks have slouched down, and wonder if they don't bother him.
Starry