Zener diodes would be much better. BUT they can still be noisy if you used the wrong voltages to add up to what you require. Zener diodes are a whole world of their own, having different characteristics with different voltages. They can supply or better worded. regulate over a wider current range than a neon pilot lamp. There are many good books on zener diodes if you really want to learn about them. Be warned, you will find 10,000 books on them, most of which have the same information.
My advice ( only mine
) is to follow the circuit as is, and see how it works. When you buy NE2's buy a dozen, or even 25 and test them to get as many "similar" ones together to use for your project.
Joe