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the nominal current for the end filaments is not stated - unfortunately,
if you can make a constant current converter to feed the lamp, DC, up to 0.4A, 45V max, (a flyback would do, off 12V DC or so) then you need only heat the negative end filament to make the lamp glow. One upside of this is you can turn the lamp around when the 1st filament goes west ).
In normal AC ballasted operation the lamp current is the same as the end filament current, you will have to experiment to find the lowest filament current that will work, and the associated voltage when the filaments are hot, a buck converter off the 12VDC with a current limit should assist here.
It appears to be similar to a fluorescent tube which uses a heated filament at both ends to ionize the mercury vapor and start the arc through the tube which drops about 45V, and requires a ballast to limit the current to 0.4A.
After the arc is started, the filaments are normally turned off.
I presume you have found out that 12V DC supplied fluorescent lamp ballasts are an off-the-shelf product, available for different lamp power levels. They are e.g. used in boats and caravans. 12V AC operation may be possible with just a bridge rectifier.
Normally the current through the filament is turned off but still connected to each side of the supply. The ionisation current keeps them hot enough for emission. There are exceptions when 'instant on' is needed but for the most part, the current loop through the heaters is broken after a few seconds leaving the ends with supply voltage between them.
Note that the tube in the link is a UV sterilization type, not one for general lighting. I use similar ones here and the heaters are definitely turned off but still glow hot from current through the tube.
respectfully - the only way the filaments can glow hot - evenly - is if there is a defined thru current in the filament - I'm not sure the current in the gas can achieve this ... ?
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also it is a well proven effect in DC powered fluoro lamps that the positive end filament does not degrade over time as the neg one does ( as the neg one is powered to glow slightly ) - allowing the tube ends to be swapped when the neg end filament expires - effectively doubling the life of the tube compared to AC powered installations ...