They typically run at 1mA which is low enough just to use a single resistor to drop the current directly from the mains. The voltage across the neon is about 90V when it strikes and 60V when lit, so theoretically the power dissipation of the neon lamp is just 0.06W. However with the resistor loss included it's about 0.1W at 110V and
0.25W at 240V. Virtually nothing in other words.
They also have a very long life which can be extended further by deliberately running them at a lower current like 0.5mA. When run in this manner the arc may become unstable after a time and start flickering up and down the electrodes. (Which is quite a nice effect actually.)
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