Well, two things that are now known is that the pulse coil is working and the kill switch is not causing a loss of spark.
Presumed to be working is the CDI unit - it is discharging into the coil and the coil is producing a spark.
Not known is: the condition of the grounding of the engine to the frame, the grounding of the coil to the frame, the functionality of the coil and CDI charging coil. The coil may be at fault if the CDI unit is discharging an approximate 100 volt peak voltage spike into the coil and the coil is not raising the voltage of the 100v spike to appx 30,000 to 40,000 volts. The charging coil may not be generating the necessary appx. 45 volts that the CDI unit amplifies and rectifies into DC to charge the capacitor to the required appx. 100vdc.
I suggest you do one of two things; either buy or borrow a meter with a peak voltage function to measure the output of the charging coil, CDI unit and primary coil or start throwing parts at it. If you decide to start throwing parts at it, start with a stator, they have the highest failure rate or try a new primary coil as they are relatively cheap and easier to replace.