A zener will behave exactly the same as a regular diode in the forward direction. That means when the anode is more positive than the cathode current will be allowed to flow from anode to cathode once you get past the knee voltage, roughly 0.6 to 1.0 volts. This is often referred to as the diode voltage drop. In the reverse direction where the anode is less positive than the cathode both the zener and regular diode will block current flow. So no current will flow from cathode to anode. The exception to this for a zener is when the reverse voltage gets to Vz, the zener voltage. At that point the zener will allow reverse current to flow.
A normal diode will do this too at the reverse breakdown voltage but it is less controlled and could lead to diode failure. When you see a normal diode rated at 1A 50V it means it will breakdown at a reverse voltage of 50V.
In the ZW the zener will allow some current to flow in reverse at the voltage peaks. This shifts the whistle voltage slightly and augments the parallel resistance in the ZW that allows AC to flow around the diode. The goal is to still supply AC to the motor while adding a DC offset to pull in the whistle relay.
The ZW also adds a 5V winding when the whistle is engaged. This compensates for the higher forward voltage drop of the original rectifier compared to a silicon diode as well as current used by the whistle motor. You don't want the engine to slow down or speed up when the whistle is blown.
With the variety of whistle voltage circuits in various old and modern transformers and old and modern whistles it is all rather hit or miss.
