Fairings typically go through an oscillation stage immediately after separation and then a relatively low rate tumble ‘away’ from the rocket. That’s due largely to the fact that there’s intentional stresses in the encapsulated configuration (plus springs) that push the halves away from the payload/rocket—the det cord and pyro devices that actually break the halves apart can’t safely separate them on their own. The post separation motion is a very understood and modelable phenomenon, and so it’s probably pretty easy to derive the minimum amount of thrust/vectors required for a system like cold gas to stabilize the fairing halves. They’re so big and so light that it seems quite feasible for thrusters mounted on the top or bottom to right the ship pretty easily.