What Umberbr was referring to was a serpentine belt which drives the accessories, not a timing belt… If this is a 2001 Toyota Celica GT I am going to assume it has a 1.8L engine…
On the 1.8 the belt tensioner is known to go bad… Not saying that is your issue just yet.. You are correct, it has a timing chain driving the camshafts…
The A/C light on a Toyota will blink when it is low on refrigerant/rapid cycling of the A/C Compressor… It may work in the cool mornings with a cool engine, but not later in the trip when the engine heats up or the day heats up…
The U.S. is now going through a “Polar Vortex” with cooler than average temperatures… that is why it could be working now (if you are in the U.S.)… A/C works at certain temperatures and humidity…
Since the A/C compressor on this is a NipponDenso unit here is what I advise, and I don’t say this lightly… Get one of those A/C freon bottles they sell at the auto parts store and set the temperature on the pressure dial to the ambient air temperature… Hook it up to your low pressure port and check the pressure… I would bet it is low… The reasons are too numerous to explain, but if you want A/C the rest of the summer try it… Add refrigerant until it meets the ambient air temperature you set (it is a rotating wheel over low pressure) which should be between 20 and 45 psi. Also, do not overfill… Refrigerant is not like sex and beer (more is better)…
Toyota A/C systems leak in different locations… But very slowly… This is the only reason I advise A/C fix in a bottle and it should be the only time it is used….
Let us know how it works…
-Karl