ORIGINAL: downunder
It's quite possible it's just a reaction from the model to the firing impulses from the engine. Every time the engine fires the torque reaction feeds back into the model and maybe the wing or tailplane is acting like a tuning fork and resonating. Sometimes just using a different prop can cure it by making the engine run at a different speed at idle.
Downunder is correct.
This is known as "Harmonic Vibration"
Everything in the world wants to vibrate at a certain frequency - This is how a Microwave oven works. The magnatron sends radio waves at the same frequency at which water molecules vibrate. The molecules vibrate and create heat and your food cooks.
Or look at Downunder's analogy to a tuning fork - If you have a tuning fork which is tuned to an "A", and you play an "A" on an instrument, the tuning fork will vibrate because it is getting hit with vibrations that are the same frequency at which it is designed to vibrate.
So what's happening is your engine is vibrating at the same frequency that your tail wants to vibrate. Now this can be caused by only one thing - the vibrations put out by your engine.
Being rich has nothing to do with it. An unbalanced prop MIGHT be the culprit, so try checking it's balance first.
Otherwise, your only options are:
1) Idle at a different RPM
2) Redesign your tail so it vibrates at a different frequency
3) If the prop is balanced, try unbalancing it slightly and put the heavier end opposite the piston at Top Dead Center.