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Does he actually have to be on screen in order for it to count as looking at him, or is it okay if you can't see him behind the boxes?

As long as he's in front of you, the boxes won't technically block your sight of him because the programming is very simple.

It seems as though there's a range for him staying in a spot because I walked away staring at him and when I got far enough away he disappeared and moved somewhere else, is this supposed to happen?

Eventually you'll be far enough away (past the draw distance) where he know's you can't see him even if you're technically looking in his direction.