Just a suggestion. The role of secondary winding and switch S1 can be a shifting of core magnetizing curve. When S1 is closed the DC current through secondary shifts curve toward more linear part out of saturation.
Look at dots on windings.
The top circuit generates a magnetizing current in opposition to the current from the bottom circuit. This prevents the core from saturating due to the the bottom circuit pulsed DC current and allows the signal from the bottom to be transmitted through the transformer. So switching the top winding would appear to have the effect of turning the output signal on and off. But that's just a guess. :???: