Haven't noticed this before but the radiator fan comes on when the switch is turned on. Even before the car is started. The fan continues to run as long as the car runs. Is this normal or could there be a switch or something not working?
Depending on what year your car is, what engine it has, and whether it has A/C or not, there are several different reasons why it may be doing what it's doing. The '84's are unique beasts with two speed fans, the '85 to '87's regardless of engine type and the V6 '88's all have single speed fans and have the same circuitry, and finally the '88 four cylinder cars fans are controlled by the ECM so you need to state what year and engine you have. Also state whether you have A/C or not and I or someone else will be able to narrow down the source of the problem more easily.
Watch your engine light before you power on the ignition. If it does not flash at least once when you turn it on the problem may be the chip as when there is a problem with it the fan will come on as soon as you power up.
I wired my A/C so that the fan will only come on with it if it has a sufficient amount of refrigerant in it, so in my case if I disconnect the pressure switch neither the fan or the A/C will kick in but that would isolate where the problem is.
Check to make sure the green wire with white stripe at the relay up front near the left headlight is not shorted to ground.