Maybe the wiring to the idle switches is flaky or the connector is not making a good contact with the posts.

When you turn on the ignition but before cranking, does the oxygen sensor light come on ?

Here is the reason I am asking:
Oxygen sensor is continuously monitoring the oxygen content in the exhaust and sends the signal to the computer and the computer adjusts the air/fuel ratio accordingly. This is a feedback system and if the signal from the oxygen sensor is delayed in any way (just a sluggish response) then the feedback system will oscillate. So either the computer is getting the wrong signal or the actuator, i.e. the governor (the small black part that sits on the fuel distributor and has wires running into it), is not obeying the computer's command properly. Check the wiring for oxygen sensor as well as the governor.

If you stare at the air sensor's plate, this plate is not moving when the RPMs oscillate, right ?

Unmetered air getting into the intake may also cause errors in air/fuel ratio calculations. You can spray some carburetor cleaner around the air sensor's base, and other places around the intake manifold, and see if RPMs are affected. But periodicity points more to the oxygen sensor's feedback loop.

Saumil

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Saumil S. Patel