My first thought was something was shorting the Diagnostic Connector Link (DCL) where you short the A B terminals to get the light to flash. But then if it got shorted with the car running, the CEL would flash at different rates depending on if it is in closed loop operation or not.
It's not doing that.
That means the computer is probably turning on the light. But with the engine not running and key on, it would still give you codes and it is not. So you have a computer problem. It may or may not be the computer itself.
You need to check ALL the power and ground leads to the computer. You have more than one of each.
Some early cars did in fact have a problem with the coolant temp sensor. If it has a round plug it is the original style. If the plug is rectangle, it is the updated replacement style.
The original leaked coolant which wicked all the way through the wiring harness and actually leakes coolant into the computer. Some were so bad the computer would leak antifreeze. Coolant and antifreeze do not get along. Sometimes you can open the computer case and use electrical contact cleaner to gently clean the computer boards. If you have the coolant problem, and the cleaning won't help, then you have to replace the computer.
