In your flash tube there is a large capacitor connected between the pair of big electrodes in the ends of the circular tube. When ready to operate, there is a large (lethally large!) charge waiting here to be discharged through the gas filled tube. The capacitor charge voltage (several hundred volts) is not enough to initially start the discharge.
To start the discharge a a very high voltage (10 000V or so) spike is applied to the trigger wire that is wrapped around the tube.
Your problem is likely that the wire electrode is too close to something. The trigger pulse shold not spark over anywhere outside of the flash tube. Find where it is sparking and try to increase the distance of the trigger wire to the other feature. A sharp end point sticking out from the trigger wire can also cause this wrong-way flashover. This external sparkover lowers the trigger voltage so it is not enough to ignite the tube.
As others say, when the unit is ready and has not flashed, it contains a lethal electric charge. This is for real, it is not just a routine consumer warning. Be careful.