When the load draws greater current, it reduces current available to the auxiliary winding... causing a drop in voltage from the auxiliary. At least that's one way to look at it.
Or does greater load watts cause higher flux levels in the transformer (and higher voltage in the auxiliary)? Another way to look at it.
Sorry I don't have more experience. One similar experiment I tried was to wrap a few turns of loose 14 gauge around a small transformer. The 14 gauge carried power to a refrigerator. I hooked up an led to a winding on the transformer. When the refrigerator motor turned on, the led lit dimly.
This suggests you can likewise experiment with a few loose turns of wire around a transformer. It should act in reverse fashion, that is to generate greater or lesser mV AC in response to power going through your transformer. Sufficient to use as a feedback signal.