I don't like the idea of color shifting at all -- but if it must be done, it should be restricted from the amber to red range in observance with vehicle lighting laws. In the USA at least, Rearward lights are only allowed to be red or amber. Forward lights are restricted to white and amber for normal vehicles. Forward-facing red is for emergency vehicles, blue is reserved for police, and green is never used on vehicles.
A better solution IMO would be to use amber for the 'turn signal' lights, red for constant-on tail lights, and have the existing red lights jump to higher intensity, or turn on additional red lights when braking. This is essentially what cars do.
For that matter, variable intensity brake lights based on rate of braking is always something I've thought would be a good idea for both vehicles and bikes. Quite often drivers approaching a stopped or slower car will gently tap on their brakes, then at the last second realize they aren't braking quickly enough to stop in time and SLAM on the brakes. A sudden change in intensity on the brake lights would be helpful for all the drivers behind them.