Is there terminology for perceptual illusions at the moment that figure-ground reversal occurs?
There are many such illusions. It mostly belongs to pattern-recognition and gestalt psychology. From German it means "shape", "form", "essence". To answer your question, I think, here there are illusory contours (when you watch and understand an illusion) and lateral inhibition (when you have got new understanding of the picture and compare it with previous form).

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