Norcold 1200LRIM won't stay off

As another stated, you are getting AC ripple thru the DC. Since you have an Inverter/Charger, that will rule out a Converter cause. Now, there are a few other items that can cause this type problem on OLDER units. The most often cause is a defective Fluorescent light ballast. Are you doing your tests with ALL the interior lights OFF. If not, you make sure all the interior lights are OFF and then reset the Refer and see if it will now turn on and off correctly. IF you change out both rear and Optical boards to current, the odds are the problem will go away as those are the only 2 items that will be affected by AC ripple and causing your problem. Now, you state you spend upwards of 2k or more replacing a functioning refer for this problem? Online it appears the Control kit for your refer is from $225 to $350. Also, what I would do, is run a simple 12 volt ON/OFF lighted switch from the rear of the refer to a spot inside the RV and just KILL the power to the refer when I wanted to shut it down. WHY spend a lot of money for a simple solution????? Doug