Where on the stab's MAC is the pivot located?

On most full-size jets, the pivot is located at about 20% of the MAC. If the pivot is aft of that at or near 25% of the MAC, the stab will start to 'wander' if the control is not mass-balanced.

I flew a model of MiG-29 that had the pivot incorrectly located and the stabs did not want to stay centered in flight. Since it was a small-ish model, the control imbalance was not able to overpower the servo, so this was not an issue.

You can test this. Remove the stab and attach it to test fixture that will allow the stab to rotate freely. Then, have someone drive you down the freeway and stick the test fixture out the window into the slipstream. You'll see immediately whether the stab is dynamically balanced.

Then, mass-balance the control and repeat the test. You should see a dramatic change in how the control behaves.

Dan