Your covering-one-eye thing works particularly nicely if you use it in a place where you can see the tops of lots of trees at various distances overlapping each other. Cover one eye and suddenly all those canopies become one depthless blob, like it's one gigantic treetop.

It sounds like you might be interested in experiments with deliberately redirecting your eyes. There's lots of interesting phenomena you can achieve by pointing one eye at one thing and another eye at another thing. Here's a paper of mine which can serve as a sort of stepping stone into this wide unexplored field: https://philpapers.org/archive/ALEDSK.pdf