Gerald, good point in drawing my attention to the main capacitator.
My idea though was/is that in case the main capacitator won't have it's full capacity any longer, the voltage will finally still rise up to the charging voltage. The lamp will glow (though no longer indicating the fully or rather sufficiently loaded state of the main capacitator).
However, in case that loss of capacity is due to a "electrical leakage" of the capacitator, I guess there might be a situation where at the capacitator is a lower voltage, still sufficient to flash the flash bulb but not to make the neon bulb glow.
This all makes me realize I did not yet consider sufficiently the issues of capacitators...