It's a classic fault which LOADS of mk2's have, the light is the low coolant level warning. Normally it's the sensor that gets covered in crud after all these years but it could also be a dodgy contact in the instrument cluster. On a gti the sensor should be screwed into the top of the expansion bottle, remove it and clean the prongs. If it's still bad the replace it, it's a 5minute job. If the problem still persists after that then you'll have to clean all the contacts to the cluster.
