I have to correct my explanation a bit. Checked my notes again. The bank of LED lights may actually be behind the bottom painting, not in front of it. So the "meat" in the sandwich may be misplaced in my analogy. The headless painting is technically backlit (although with LEDs they may almost be enmeshed into the painting, I don't know.
So: lit from the front, you see top layer (normal), lit from the back, you see bottom layer (headless), and the two layers are very close to each other and the switching back-and-forth of the lighting is extremely sophisticated so that you can't detect the change other than seeing the differences between the two paintings, both of which are on a sophisticated (probably specially designed) form of scrim-like material.