I had exactly the same problem on my EB fairmont and this is the way to fix it as one of the helpfull people on this site told me:
Is this manual climate control or automatic?
If is automatic, does the light actually change?
If its manual, then my first port of call is the vacuum supply. In your engine bay, on the firewall near the washer bottle you will find two thin plastic tubes coming out. One is black the other is green. I forget which colour is which, but one (probably the black) is vacuum supply. The other is heater tap control.
Check they are both connected. If its manual climate, then i'd say that the supply tube has been dislodged. this will also be true of automatic climate if the lights change when you press the buttons.
With mine it was the black vacuum hose so it may be the same as yours.