If your car is the same as later models, the sensor is located about halfway down the passenger side tank on the engine side of the radiator. If you have a selection of plugs and stoppers, you can plug the hole when you remove the sensor to change it. I just unplugged the electrical connector from mine when it quit working, and simple cleaning and replacement did not restore function.
If you want to avoid spilling a drop, siphon the side tank with a thin vinyl hose into a gallon jug. That will get you down below the sensor.
When my '92 SSEi sensor failed, I was too cheap to replace the part, and tried removing it and cleaning it. Worked for a while then sent the same false signal. I eventually just unplugged the sensor. Light goes out when you do. Then you check your own coolant level.
Here is a little tool I made from a nail to help unplug the electrical connector and the rubber stopper for plugging the hole if you want to try to clean it.