clean the float
First, assuming that the level is at the full mark when the engine is cold.
Have you checked the concentration of anti-freeze? It should be at minimum of 40 percent and a maximum of 60 percent. If the concentration wrong, the specific gravity will be wrong and the sensor will not float. If you use an inexpensive anti-freeze tester, make sure the anti-freeze is not hot. Otherwise, the reading will be wrong.
Start out by confirming that if you hold the de-gas float near the top that the radiator light goes out. This confirms the basic warning system is working.
This is a problem with many Fords (not just the Mustangs). The sensor will get “water logged” and not float as well. When the coolant level is low, the float sensor will stick to the magnet. Sometimes it will not have enough buoyancy to free itself. Also, if there are any deposits stuck to the float, cleaning can free it up enough to make it work.
To really clean the de-gas bottle, remove it from the car. Rinse thoroughly. Refill with vinegar and SHAKE. Let soak. Rinse and let air dry. This may also dry out a water logged float.
Optionally, try “helping the float” to the top. If stuck on the magnet, your help may it needs. Obviously, if the level gets low, it will stick again.
Lastly, the entire de-gas bottle can be replaced. The de-gas bottle is permanently plastic welded together. It is not practical to separate the plastic welds to service the float.