Simple issues...your coolant level sensor is corroded...does that with age.
Look near the bottom of your coolant tank and the sensor has a electrical connection to it. Most likely it has gotten to the point where the coolant now seeps onto the terminal contacts and is causing the effect you describe.
As a temporary measure, you can clean the contacts and the sensor and get the light to go off.
This may get you by for a few weeks to a few months when the light starts to come back on, but eventually you will have to replace the sensor.
Fortunately it's not expensive. $40 (I think) and you can replace it yourself within 15 minutes. Did mine last year when the same issue occurred.
Check Fastlane at the top of the page to obtain the part.
