At this point the value of all this is anything I learn because these devices cost close to nothing. I need to leave this thing alone because the quality is not good and, for example, the helicoidal zapping wires are aluminum and break easily from flexing.
Magnetic ballasts are better at smoothing current but they consume quite a bit of power and let it off as heat. I guess that is why they also put a resistor in series with the capacitors.
With what I know I feel I might attempt to build a new one or rebuild an old one. The voltage pump is easy and the light can be anything.
In my repairs of different products I am finding quite often a certain incompatibility of components which are technically good and are supposed to be good.
For example, I have USB cables and chargers which are all good but they might not work when coupled in some way so I have sets of cables and chargers assigned to each device and I know they work.
Also with components in devices. Components A and B should work together but they don't. Components A' and B' from a similar device do work. I exchange B with B' and now everything works. It is probably a matter of marginal specs.
I think this is probably the case here. The tube is not bad, the starter is not bad but they just don't work together. Probably a matter of specs being at the limit or outside.
Also, probably the device was tested at the factory and worked well. But maybe now I am using it with different voltage, different temperature (it is extremely hot here), who knows what else may be different.