Fluctuating Idle RPM - '87 260E

I appreciate any feedback on this.

My car is occasionally idling between 600 and 1500 RPM. It will go up and then drop off suddenly back to normal. Sometimes it will stay at 1500 for more than a minute. It will sometimes idle at 1000 and slowly work up to 1500 RPM - but never higher than that. Then it will sometimes idle where it's supposed to for many minutes at a time. I should say that at every RPM the engine runs smooth and there is no hint of stumbling. The air fuel mixture seems perfect.

The problem is unnoticeable anytime the accelerator is revving the engine past 1500 rpm.

The reason I am running this past the forum here is that I'm very sceptical of the diagnosis of my repair shop. They say the problem is the fuel management computer. I asked them if they meant what is often called the ECU. They said Yes, that's the part. They are going to get me a used one $500.

I've had the ECU go out on other cars. The symptoms seems to reflect the wrong amount of fuel for the available air flow resulting in a very poor running engine, stumbling, and gas smell in the exhaust.

Could it be the ECU? I'm thinking idle control unit or control valve.

Steve Hawkins