The early systems did not have the capability to "store" a code. The way it works is, if the ECM "sees" an issue that requires it, it will turn the Check Eng/Service Eng light on. IF the issue goes away while driving, the light will go off, and the code will disappear. For instance, if the ECM sees an issue with the TPS(throttle position sensor) that is maybe out of spec, the light will come on, and a code will be available. If the TPS problem goes away, then the light goes off, and the code is gone also. A TPS can have a very small "bad spot", usually right at the place it would be while cruising on the highway. The accelerator pedal may stay in the area just long enough for the ECM to see it is out of whack, and turn the light on. If the TPS bad spot is fairly large, the light may stay on for a while. Once the pedal is moved out of that particular "bad" spot, it will again start reading properly. The ECM will now receive the correct reading, and, after a certain amount of time, it will extinguish the light, and delete the code. Some problems need to be in effect for a certain amount of time, or recur several times in a certain amount of time, before a code will even set. This is why it's best to try to scan for codes while the light is on. If the light is on while driving, and you scan it, you'll be able to pull the code. If you turn the key off, even while the light is on, the code will not be stored. NOw....if you have a "hard" failure, meaning an issue that is occurring just by turning the key on, then you'll be able to see that particular code. For instance, if you were to unplug the flat connector going to the distributor, and turn the key on, the ECM would recognize that it doesn't get any feedback from the ESC system, and it would set a code for that.
Hope that helps.
Later GM systems(I think '84-up) do have the ability to store codes, even if the light goes out, and the problem is not present at the time, but the '81 will not.
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