Most aircraft with air-to-air radar, such as fighters, have the radar on and use it from takeoff to landing. That said, there are limitations on the number of targets it can track, and, without rereading the specifics of this accident, I think the F-16 had just made a descending turn a dozen seconds or so before the midair. That's not a lot of time to pick up and analyze new traffic as it comes into the radar's sight, especially when single seat and giving more concentration to the instrument approach procedure.