I could never see the hidden image in those things. I get how it can “lift out” when it all comes together. But however long or how I stare at it, I can’t see it.
Once or twice, years ago, I was able to focus "beyond" these pictures and see the thing described. But that was before my old eyes stopped being able to focus properly.
These days, the only way I can see something 3D is to cross my eyes a little bit and focus "before" the picture (like this one). I get the 3D image, but it's inverted, in other words this teapot appears as a hollow space in the shape of a teapot, carved deep into a background of colors.
It's even weirder that way than the "right" way.