I think your drawing has the switch in the wrong wire - it should be in the link between the filaments.
That should at least produce a momentary flicker, though it would need quite a bit of voltage to be able to sustain light!
It is using the back EMF from the inductor to create a high voltage spike and "strike" the tube when the current path through filaments is broken.
I've never tried that - though I did run them off conventional xenon strobe tube circuits, using a wrap of wire near one end as the trigger terminal.
It's quite effective when the tube is cold, but at anything other than a very low flash rate they start to conduct continuously after a few seconds as they warm up.