My initial thought was that it is somehow associated with the cooling fan(*). I was keeping quiet though as everybody was running with A/C compressor, and wasn't sure what to expect. That would explain why you have to run it around the block after running the A/C, the cooling fans remain on for a minute or two after the A/C is shut off. I was also not sure as there was never any other times it was staying on. It would probably be a good idea to confirm if it is related with the fan running.
Now, if it is connected to the fan running, I have no idea where to even start from there.
I am not sure how this could happen, as the way the PCM controls the fans, is by grounding the negative on the trigger for the relay. The entire system is usually live when the ignition is on anyway.