The sensors can go bad. A sure test would be to fill the overflow tank to the top and see if the light goes out. You might have to check the tank as soon as the light shows, to be sure the radiator system hasn't absorbed more coolant and reduced the level. Also, 'giggling' the wires, does that mean you told them jokes? tickled them? You might disconnect them and clean the contacts.
If your engine requires a 10 lb radiator cap, Google shows lots of results for a "10 PSI radiator cap." A 13 PSI cap should allow a slightly higher temperature than the 10 PSI cap, as the 10 would lower the boiling point of the coolant temperature. I'd make sure you have the proper cap, perhaps a previous owner put the 10 PSI cap on for some reason.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI