....not sure how to answer your question re switching. A bit beyond my abilities.
.....
Btw I meant to ask what you meant by 'filament' above?
I haven't found the full schematic online.
If you have it, what happens to the 3 unregulated outputs from the power supply? I'd expect some regulators are used before supplying 12V and 5V IC's.
There will also be some power switching for standby mode done by transistors or by dedicated voltage regulators.
The "filament" relates to the VFD: They are basically a triode with a phosphor to get some colourful glow on the anode, there are several parallel filaments (heated) that also serve as the cathode from which the electrons are emitted.
Between filament and anode are multiple fine meshes, one for each segment of display, they're used as on/off control grids by the display IC.