I'd like to clarify this statement of mine:
"So when it is explained that the hv spark jumps the gap ionizing it to reduce the resistance of it and have the lv source follow it...is incorrect."
I'm meaning is incorrect that this automatically just happens first without the other sequence of events. It is a fact that the HV jumps to the LV source first backwards through the diode.
The gap does get ionized to make it conductive enough for the LV to jump over the gap but only AFTER the HV jumps to the LV source first.
The only other thing I'd add to what was quoted is that the cap discharges faster by a negative resistance effect because the HV positive pressure is pulling very strongly on the LV current - so the cap is discharged against a reduced impedance or negative resistance.