The gated pulse is NOT just to build a charge on the WFC. It starts by building a charge on the coils!
The primary frequency pulse builds charges on all the coils, starting with the primary, but doesn't release it until the gate off pulse. When released by the gate off pulse, it is released by thousands, even hundreds of thousands of induced volts, both on primary and secondary when the core's field collapses.
The high resistance/impedance in the secondary circuit prevents the charge from leaving the secondary coil until the off gate pulse. Once the gate pulse is off, the secondary will generate a voltage large enough to push the current to the WFC. How much of a charge that is is determined by the length of the gate on pulse. The longer the on pulse, the higher the charge. But it will not discharge until the gate off pulse. The amount of voltage could literally be hundreds of thousands of volts coming out of the coil! A lot of it dissipates on hitting the resistance of the WFC, but a high peak to peak voltage wave will still show up on it.
The gate pulse frequency needs to be very low, possibly from 1 to 25 Hz for example, but have a high duty cycle, like 80% to 90%.