I don’t know the billboards you’re speaking of, but your description sounds like the masks you can see near the beginning of Disney’s Haunted Mansion in both Orlando and Anaheim. The masks appear to swivel to follow you. It’s a very creepy illusion. The “masks” are actually inside-out hollow faces, the thing you would get if you took a mask and hung it on a wall with the concave inside facing toward the viewer rather than the convex outside. Because of your expectations, you perceive the mask as being convex-out, as you normally would se one. But as you move around the sight doesn’t really look like a statis convex mask – it looks like a convex mask that is swiveling to follow you. But it’s really a stationary concave mask
Watch this video. The section explaining the masks starts at 4:14
