float sticks to the magnet
I have had this problem on several Fords (not just the Mustang). Over time, the float soaks up coolant thus making it heavier. My current 2000 the float works if the anti-freeze concertration is above 40%. Too much water and it sinks.
I have also had it happen where the float and post was dirty. Cleaning the tank with vinegar helped.
Had one car where the float would stay where it was. If you helped it to the top, it would stay there (or perhaps it could not free itself from the magnet).
There is no easy way to service the float as it is plastic welded inside the de-gas bottle.
Suggestions. First try to "help" it free itself from the magnet. Next try cleaning the de-gas bottle. If that doesn't work, the options get harder.
May try attaching something (glue it) to help it float. New de-gas bottle. Finally there is disconnect the switch to disable the light.