I figure that your 0.1uF and 1k parts produce a frequency of about 1.6kHz. But if your toroid has a ferrite core then it needs at least 40kHz.
The TIP122 has a saturation voltage loss of about 1.2v so each side will have a peak swing of only 2V then the output into a transformer that works will be only 40 turns/10 turns + 10 turns= 4V peak. You need many turns on the secondary to get a high output voltage.
The 0.5uF capacitor parallel with the neon bulb with the 2.2M resistor feeding it produce a slowly blinking light when powered from DC. Get rid of the 0.5uF capacitor for the Neon to light from a high AC voltage.
The TIP122 has a saturation voltage loss of about 1.2v so each side will have a peak swing of only 2V then the output into a transformer that works will be only 40 turns/10 turns + 10 turns= 4V peak. You need many turns on the secondary to get a high output voltage.
The 0.5uF capacitor parallel with the neon bulb with the 2.2M resistor feeding it produce a slowly blinking light when powered from DC. Get rid of the 0.5uF capacitor for the Neon to light from a high AC voltage.