Edit: Problem solved! So when I first bought the car, the check engine light would come on - P0606. I took the gentleman's advice to replace the Mass Air Flow Sensor. That stopped the check engine light from coming on every 2 days. Another problem was that when I turned on the tail lights, the check engine light would come on - P0606. I also got the CEL when it got dark. So the problem was in the tail lights I concluded. I replaced the tail light bulbs and that solved the problem. When I took the old bulbs out, they were rusty. Definitely going to check some of the other connections. Cheers.

The ECM is definitely the prime suspect here - but before I'd replace it, I'd go though all the connectors to/from the engine to the ECM, check for corrosion, looseness, use some contact cleaner on them, etc. That might be a source of problems, and it's always a good idea to check the cheap fixes first.

Common Problems That Trigger the P0606 Code

• Defective PCM (Power Train Control Module)
• Defective PCM wiring/connections
• Defective PCM ground circuit(s)
• Defective PCM controlled output devices
• Defective CAN bus communication

https://repairpal.com/obd-ii-code-p0606

Check the PCM connections first. Make sure they are clean. 

Do not replace the ECM. For some reason a bad A/F sensor causes this code. It is a known issue with Toyotas. Replace the upstream 02 clear codes and you’ll be fine. 

Gentlemen:

Background information:

1. 156,000 miles

2. This Corolla is one of the affected vehicles from Toyota's 2010 NHTSA's report with the ECM containing a defect. The ECM may have been improperly manufactured. There is a possibility that a crack may develop at certain solder points on the current circuit board. Harsh shifting could result, or the engine may not start.

3. p0606 code comes on after 2 days or earlier of driving. Result is loss of power. When I clear code it runs fine.

4. Vehicle was in 3 collisions.

5. Toyota dealership replaced the transmission 1/8/22. Also checked engine/powertrain computer/module (Carfax). Vehicle sold at Auto Auction.

6. When I turn on the headlights, a p0606 code immediately follows with loss of power. I clear it and it runs fine. (Not making this up)

7. No other codes come on.

Question:

My inclination is to order a pre-programmed ECM and have my mechanic install it and then proceed from there. Is this the right course of action to take? I thought at first to have a mechanic check it out (connections on ECM, grounds, etc) (feedback from other question). Is there anything else that could be checked out or should I just buy the ECM? Also, I have not reset the computer to factory settings to see if other codes come on but so far none. 

Posted by: @cmoritz

I thought at first to have a mechanic check it out (connections on ECM, grounds, etc) (feedback from other question)

It is a good idea. Although according to the symptoms, odds are you need a new PCM.