It is normal for the kill wire in a points ignition system to have a peak voltage of hundreds (say 150-300 V) which is enough to produce a visible spark, though not a very long one - certainly not 2 mm.
So, I am back to not knowing what you are unhappy about. With the kill wire isolated (i.e. not shorting to earth, or anywhere near earth) does the magneto generate a spark from the plug-wire to ground? (Don't use a spark plug, in case it is defective.) If it doesn't, you have an ignition fault, but most likely an ordinary one. Most such faults are because the breaker points aren't correctly gapped or the capacitor is faulty. The remaining few are just about certain to be shorts to ground or defective coils.
There is no spark on the HT even if the kill wire is isolated or earthed. Ignore what I said about 2mm, redid it and it's under 1mm.
Can the cap be easily replaced? I have a couple of spare caps from other trimmer engines... buying a new coil or original cap is out of the question, as most spare parts sites want $40 for the cap and $60 for a coil!
