Before you unplug anything or buy anything new,
this problem does come up a lot in Mustangs,
This is the Fix for 99% of the problems,
Take out the sensor, ate the bottom you will see 2 Metal Spades (looks like a fuse or spade conenctor)
CLEAN THEM!!
Get some good quality brake/carb cleaner if you have to,
Give them a good cleaning, use a wire brush if you have to, make sure you dont snap them off,
and Bingo! Problem solved,
the sensor just gets dirty most of the time and throws the LOW COOLANT crap in your face
hope that fixes your problem