Might be worth trying it on a higher voltage if you can..?

Interesting, it's strange the filament lights without the mercury arc as I thought these were always fully in series. Sometimes the mercury arc can look very dim at start with the low pressure but that changes quickly. In all the filament ballast lamps I have the filament doesn't light until the arc has struck if the voltage is just too low to sustain the arc they flash sort of randomly.

Not sure if applying a higher mains voltage is a good idea. If the filament lights up before the arc tube then that's definitely a 120 V SBMV lamp, in which case the filament is already overloaded at that voltage. The arctube not striking up could be caused by residual impurities if the lamp is not EOL. Best course of action in that case would be to apply some high voltage (at low current) to the lamp (with e.g. a Tesla coil) in order to force some ionization in the arctube. Charges leftover can help with ignition. Another possibility for your problem is a fault such as a break in one of the wires inside the lamp.

Max, so in 120V filament ballast lamp is there a potential divider arrangement with the filament? Is this to increase the mercury temperature for lower voltage for striking? Perhaps it's a bit like my difficult to start black light and may need run for a while, in which case some sort of external HV start would be worth doing.

Not sure what you mean by "potential divider arrangement", but in 120 V SBMV lamps the ballasting filament and the filament electrodes inside the burner are connected in series across the mains when the lamp is cold. The role of the filaments in the burner is to produce electrons via a thermionic process. In essence, the lamp is started a bit like a switch-start fluorescent tube.

Just meaning that there is a resistive path of multiple filaments from live to neutral without the lamp being struck. Think you have answered that in there being pre-heated electrodes within the arc tube.