The Powerex device is not a Sidac.
It is a Silicon Bilateral Switch.
Similar to a Sidac except highly symmetrical in operation which can be modified by means of a gate pin.
Not sure what you mean by subtracting gate voltage?
As a bilateral device meaning it can conduct either way. There is no anode/cathode hence calling either side terminals 1,2.
Depending on your circuit wiring, threshold of plus or minus 8 volts w/specific hold current is needed to fire up the device.
Look at the characteristic curve. Gate break over voltage on either side and once turned on, it almost behaves like a short.
Being a symmetrical device, having the gate allows it to cut the Vs by 50% vs not having a gate and just assuming they are perfectly symmetrical and the centre voltage Vs is 1/2 (Vt1-Vt2)
So an enhanced SIDAC if you like.
So it's like a potentiometer with its adjustable center tap and 2 extreme terminals? The voltage drop between the tap and one of the terminal determines the voltage breakdown for that side of the device.