One clarification to my above reply:
If I recall it correctly older Neons used to draw less than 1mA from about 100 - 150 V supply which makes it about 100 – 150 mW per bulb in the worst case. I think that about 100K series limiting resistors were commonly used (the value of the resistor varies with the voltage). Depending on your input voltage to the converter you should draw 25 – 35 mA from 5V and 10 – 20 mA from 12V input. The estimated current draw includes generous losses in your system.

Regards,

Nick