Two-toned Strobe Beast
Here is a fictional color changing animal that is reasonable and not too far from a standard mammal plan. Start with a porcupine.
Some quills are strikingly two-toned.
The Strobe beast has two toned quills also, but longitudinally. Half is black and half is white, like this dog's claws.
Porcupine quills are modified hairs. They are mobile and the porcupine can raise and lower them. The Strobe beast does not raise or lower, but can rotate its short two-tone quills 180 degrees, like a human wrist or head. The short quills lie flat along the body.
Quills can rotate from black side up to white side up and back in a split second: thus the name "strobe beast". The beast can be black or white or shades of gray. It could be, if it chose, two toned like a tapir.
If you allow more precise control of stretches of quills the strobe beast could make circumferential rings and patches like this genet.
Not only could it have patterns it could make the patterns move. The strobe beast could make circumferential rings of black and white move along its body. A creature with contrasting rings moving along its body would be very confusing to watch. It would be hard to tell which direction the creature was moving. A black strobe beast could lie still and move a patch of white back and forth along its body, drawing in small predators in the manner of an angler fish and then catching and eating them.
The strobe beast cannot turn green or magenta. Just black and white and combinations.