Engine light starts flashing or comes on steady when left idling.

No sense guessing, recover the codes! Any auto parts store can do this for free. Clearly there is a recurring problem setting the code and having an actual misfire confirms it's a real problem. Disconnecting neg cable only reset ECM but as problem came back, that isn't a good solution.

If possible, run an OBD2 scanner through your OBD2 port and see what the code may have been. That will help better pinpoint exactly what the check engine light was trying to tell you (if your CEL doesn't come on, drive around for a bit until it does come on, then run the scan again). Now, if your check engine light only comes on when idling, the code *could* be related to your Idle Air Control Valve, since that regulates air flow when your car's engine is running but isn't moving (aka, idling). Also, disconnecting the battery may remove the codes/CEL temporarily since it "wipes" them from your ECU's memory, but they may come back on. Also, what do you mean by "there is a misfire in the tailpipe?" Like an irregular noise or pops coming from your exhaust? Is there any strange noises or smells coming from under the MIDDLE of the car (where your catalytic converter is located)? Finally, are you noticing any decrease in acceleration or gas mileage?

The light has never came on while driving, only when idling for 10 min or longer. No decrease in acceleration, mileage. There is an irregular popping coming from the exhaust. No strange noises or smells either. It has good exhaust flow.

Gotcha! Thanks, this context helps. Two questions/suggestions: 1) Does the "popping" only occur at idle as well? Conversely, are there any "pops" when you accelerate or let off the throttle when the car is moving?, and 2) Definitely run an OBD2 scanner once you have had the car idle for 10 mins or longer, so we can see what the code is. Then, you can reply back here and we can look it up to see exactly which part or component may be at fault!

I ordered a Ktool U-480 scanner, it will be here next week. Pops only at idle, no pops when I accelerate or let off. I just don"t understand why the light only comes on when it has been idling for a while and that is the only time it misfires.

Great! The scan will yield us the best possible idea of what's going on. It does sound like its related to the Idle Air Control Valve (IAC), since that system is what directly controls your engine's "idle" speed and keeps the air mixture and flow stable while the car is not moving (since there is no air rushing into the air intake and throttle body). This also could explain the "pops" or "putters" in the exhaust, since your IAC may not be regulating the air flow properly, and your exhaust is struggling to get the spent gasses out.