There are 2 oscillators, one on the left xformer to reach something around 400-600V from 12V, then a low frequency oscillator that discharges the 15microF 700V cap into the right transformer giving a few kV pulse on the output.
Step-up is something along these lines:
BD911 is biased into conduction through R1,R2 and the small secondary winding on your schematic.
Once enough current has flowed through the primary winding, a voltage will show on both secondary windings, the smaller windings being in reverse on the BD911 base will stop it's conduction until field in transformer is insufficient, then cycle repeats.
BC547 is there for voltage regulation, limiting BD911's conduction once secondary voltage is high enough.
220nF is either there for setting oscillation frequency or as capacitive voltage dropper for charging the reservoir cap. (Less heat dissipation)
The time constant for the fence pulses is set by R5 and 10microF cap, once diac voltage is reached a pulse occurs then the 15microF cap must charge again.
For testing you can isolate the 2 functions by breaking the circuit after the 15microF cap. If voltage ramps-up there you have problem on the pulse side.
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