Low Coolant light question:

'92 Park Avenue, "plain jane" model
Will the "Low Coolant" light go out as soon as coolant is added, assuming the level reaches up and above the sensor prong in the radiator, or does the ignition have to be switched off and back on again for the level sensor to reset? I can add coolant and fill the reservoir all the way up, it will then overflow to the radiator, and when I check the radiator level itself, the coolant is all the way to the top, but the light stays on. I then cut the engine off, and restarted the car, and light flashed as a test like normal and stayed off, until I drove around town for about 5 minutes, and then itcame back on. The resevoir tank is still well above full, and when I removed the cap the radiator cap, it's full as well. Sound like a bad sensor? Or does it sounds like I need more coolant, so more can overflow into the cooling system? One other thing to add, even if the coolant really is low, the temp gage is still reading at normal operating temperature:screwy: , so I'm not concerned about overheating. Thanks for the help!