Sounds like a faulty water gauge. Honestly I am a big fan of a mechanical water gauge and mechanical oil pressure gauge if you can. Direct reading from the engine, no wiring or electric motors or anything to flake out. I had them in my Cobra and they worked great.
2000 Mustang GT Steeda build #48. Bolt ons, suspension, Novi 2000.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.