Q: ECM stays on after key is off

I have a 1995 MITSUBISHI ECLIPSE GS (non-turbo) with a very peculiar issue. It had a parasitic draw since the day I bought it used and eventually it fried the ECM. I recently replaced the ECM and the car runs great. The problem I have is after I shut the car off I can hear a high frequency coming from the ECM, indicating that it is running or possibly shorting out. It's also notable that disconnecting the negative battery cable or pulling the ECM fuse will stop the sound and turn the ECM off, and interestingly enough, when reconnected after a few seconds it does not turn itself back on. The ECM only turns back on again when the key is inserted and set to the on position. I'm sure you can see my dilemma, having pop the hood and pull a fuse every time I'm done driving to save the battery and possibly the ECM. If anyone has an Idea of what I can check or look for, I will forever be in your debt.

My car has 119121 miles.
My car has an automatic transmission.