Old telephones are full of windings for matching line impedance, or generating side tone, providing current limiting for the carbon transmitter, and a heap of other obscure requirements.
There is no way these coils would be applicable in a electric fence energiser.
The electric fence energiser has a specific output waveform. The waveform is limited to around 4 Kv and this is done by using Voltage Dependent Resistors across the output. The waveform is generated, in the ones I have seen, by charging a capacitor to around 600 volt DC. The magnitude of the stored charge is related to the need to NOT KILL anybody. When the capacitor reaches its required terminal voltage, a switching device (SCR) is triggered and the capacitor discharges through a transformer primary winding. The transformer secondary is loosely coupled to the primary and it rings at a frequency to give a rise time of around 12 micro seconds (from memory).
When used to prevent cattle rubbing their itchy necks on fences, this arrangement is required to deter their habit. They are quick learners. They also learn quickly if the electric fence isnt giving the full grunt.
An ignition coil of the old Kettering variety usually has a resonant frequency around 1500 Hz and this gives a rise time of around 170 microsecond. The later coil types which used a series resistance were able to improve the rise time to around 120 micro seconds, but the so called 'high energy' types can have a rise time around 80 to 90 microseconds. This is much longer than the rise time for an electric fence which is around 12 microsecond.
Its all about giving a very short sharp pulse which is so quick, it doesnt cause and damage.
Again, I have to comment that your photos are really good to see. No-one on this site gives such clear and well framed photos as you do.
Hope this helps.