You have a magneto ignition, no transistors or something like that.
The flywheel makes the magneticfeeld for some time and when the flywheel has past the coil it ignite.....thats all.
Some Zenoah (like PUM260) have two coils, a red one (timerboard an HV-coil) and a grey one (HV-sparkcoil).
Into the redcoil there will be some electronics and and the pickupcoil, see the picture.
The graycoil is the same coil a CDI use and is NOT a 6 Volt sparkcoil.....this coil can't be used with a TCI !
It's also impossible to put the TCI between this coil and the killswitch, it will never work.

I wasn't see the picture of your ignitioncoil befor, now I can see and it's realy a magneto ignition.
On the flywheel there are 3 magnets, This magnetes makes the magneticfeeld., first two magnets positive, middle and last magnet negative.
This negative Voltage is also the start to unload the power from the ignition to the sparkplug.
Into the ignitioncoil is 1 sinuswaveform made by the 3 magnets the hole ignitionpower to get a spark.

Wat you need is a coil showing in picture two, a normal 6Volt ignitioncoil.