I think you're looking at a symptom, not a cause.

Alternators don't put out a lot of current at idle, so a jumpy idle causes fluctuations that you can see in the lights, etc. If it's bad enough in newer models you'll get voltage alerts and systems alerts in the cluster.

Once you fix the idle issues, I'm guessing the light issue will rectify itself (no pun intended).

If you wanted to do a quick test, just slip off the fan belt when it's cold and start it up (assuming your lumpy idle is there all the time). If it is the alternator, your idle will be glass-smooth, but I'm guessing it will be just the same.

And a partially-blocked cat will do exactly what you're describing, because the engine is running so slowly that occasionally the backpressure of exhaust will keep a cylinder from emptying on the exhaust stroke, so the next ignition stroke doesn't really ignite...misfire. That's usually followed by a rumbly kind of running, then it picks back up again. Pick up the rpms enough and the engine pressures are enough to get around it.

If you aren't in California, there are inexpensive aftermarket cats you can have welded in, Magnaflow makes a wide assortment and allexhaust.com has excellent prices and free shipping on them.

I'm not saying it is the cat, but it sounds like a good suspect.

Good luck.

Good luck.