Is a base resistor always needed in a single transistor inverter circuit?
I suggest you use any Nch FET to act as a constant current source as long as RdsOn &lt;=1 ohm or so and not use an NTC thermistor.
Inrush current limiters (NTC’s) are not intend to be run continuously as they transition at high temperatures which reduces lifespan.
I can use a simple 5mm RED AlGaAs LED as a Zener of 1.9V @ ~5mA to bias the NPN current limit to 150 mA with only a 0.5 Ohm filament current sense of 75mV (standard current sense voltage) to drive the base with about 630mV.
The pullup from LED 2.9V to base Vb=630 mV was simulated with a dim light bulb as load that is 80 Ohms hot.
With slight variations in every component, the LED to base R should be tuned between 2.1k and 2.8k if you prefer full power or reduced a tad, to extend the tube life even more x2 for every 10’C drop at some tradeoff with thermionic gain.
I invite all pro designers to peer review this design including @jonk.

One can easily soft start this with an e-cap on the gate of the FET.
The constant current power risetime is 2s/div.
This can reduce 12.6Vdc ac ripple slightly by choosing to dissipate some power in the FET.