A scene where the Doctor is fiddling with the circuit, bangs it with his sonic screwdriver in frustration and the Tardis briefly turns red would be great...
I am reminded of the scene in one of the Simpson's Halloween Specials where their house keeps changing because of the "damage" that Homer is doing to the timeline by the stuff he is doing in the past, thanks to the Toaster/Time-Machine.
Maybe the Doctor would be totally oblivious, but the audience would see it on-screen. It would only last for a few moments. Working under the console on some system supposedly unrelated to the Chameleon Circuit as the ship floats in deep space, he does not see how the TARDIS flashes from one outer shell to the next to the next, perhaps the first outer shell would simply be a red police box.... eventually back to the blue police box.
But your idea of a more brief, more simple segment might create a sweeter little moment on screen!