I suggest you remove the intake bellows behind the AMM.

If there is a tiny hole along the volutes, it can cause the same symptom. The engine will be erratic, about when it does all those things as you describe. As the hole becomes larger, it will totally die out on occasions.

I use a fluorescent light up inside. I patch a small hole with a build up of liquid electrical tape and look for the place it rubbed against. Adjust it away or place a thin sticky felt patch on the fender. Their sold for furniture legs and lamps. Rubber might look more automotive if you have a source.

There will not be any vibration of the IAC. This thing just rotates a vane back and forth about a quarter turn from a half way point.

Full power flips it hard and it will clunk. You can use the car battery but only flick the wires to each terminal. It is tight in the connector space.

The car battery has a potential of many amperes so you don not want to hold it there. I have used a nine-volt battery on the bench for the ease of it.

Happy hunting
Phil