1980 was the first year for computers on Vettes but only cars sold in California had them. 81 was the first year for computers on all Vettes.
Scanning an 81 is tough because it's the only model year whih had a five-pin DLC connector. 82 had a 12-pin. Regardless of the no. of pins, this connector is located beneath the ash tray. Some scan testers still around today support '81 but few people who have the testers also have the 5-pin-to-12-pin adapter you need to connect the tester.
Unfortunately, getting codes from that computer is going to be impossible because when, you disconnect it you erase the memory, so you're going to have to road test the car with the ECM connected to get those codes to set.
Also, because my service manual coverage is only 82-08, I cannot tell you which pin in the 5-pin connector is the diagnostic pin...maybe someone else here can.
Here's how you're going to need to diagnose the problem.
First, buy a 1981 Factory Service Manual because it has the diagnostic info you will need...along with the wiring diagram which will tell you which DLC pin is the diagnostic pin.
Next, reconnect the ECM and drive the car for a while...at least 15 minutes after it fully warms up. The check engine light may come on but it might not if someone has removed the bulb.
Then, cycle the ignition but do not start the engine, ground the diagnostic pin and record the sequence of flashes of the check engine light. If the light does not flash, consult the FSM for repair instructions.