Create 3D gifs by adding 2 lines.

Could the bars/layer even be animated, along some consistent plane, so that there's no static background part of the scene that's always obscured. (That might allow even thicker bars, if that's otherwise helpful for the plane-of-reference establishing effect, but which aren't as distracting, since the mind's persistence will 'see around' them.)

Combining these, maybe there could be more than one synthetic depth plane active at once, distinguished by color, translucence, or direction-of-motion? There'd be some perceptual dimming with all that layered-in non-native 'depth chrome', a little like looking through lenses or filters... but hey, other stereo 3D tech has similar tradeoffs.

This trick works because of the common human experience of seeing an image through various kinds of obstructions -- bars in a window, hanging strings, trees in a forest, and other similar obstructions. If we never learned to assemble an image lying behind vertical lines, the trick would not work.