How do neon flicker bulbs work? I can clearly see they only blink around the edges and they clearly have a split in layers.

This has been intriqing me for long as well.
But now I tried a brief "googling" and found this article.

tl;dr: That seems to be quite a complex effect.

tl;dr: That seems to be quite a complex effect.

Yep, it is one of the today's world paradoxes: The less useful a novelty gadget is, the more complex the science behind its workings is...

But on the other hand very often a thing with very complex science behind is at the end very easy to make. And often vice versa is true as well...

That paradox is very true, but have its exeptions: For example a big ship that moves containers around the world is very useful, but it is mostly a big piece of steel, and a small part is the engine. Not the case with TVs, those are "useful", and the science behind of what every single transistor is doing I think that even the circuit designers can't understand it at a 100%.

Well I was thinking more about things like the "drinking bird" (a low tem difference heat engine exp,oiting evaporative cooling to get the difference; otherwise a piece of blown glass filled with easy to evaporate liquid and the head end covered by felt) or "guy - girl wheather forecast mini house" (in fact a hygrometer displaying by swinging an arm so the girl is out of the house when dry so most liklely nice weather; this gadget originates more than 200 years ago and then it was really quite high tech gadget, although then crafted by many folks, as it needed just few pieces of craved and painted wood for the house and figures and few hair threads as the sensing element - so pretty much available everywhere)

Very interesting question, and thanks also for the fascinating link and the patent references!

Some further information is contained in the outstanding book "Lamps & Lighting" by Cayless & Marsden of Thorn Lighting, 3rd Edition, 1983.  This states that a special coating is employed on the electrodes, and this releases a trace impurity of gas in the vicinity of where the discharge takes place.  This causes an increase in voltage at that location and forces the discharge to move to another spot.  Obviously there must be some kind of getter in the lamps to re-absorb that gas, otherwise its concentration would build up over time.

Barium Azide is a very unstable material.  Mild heating causes its decomposition to barium metal and releases nitrogen gas.  Normally when it is used in lamps as an emitter compound, it is heated to thorougly remove all nitrogen.  Barium azide is also used as a getter in high loaded automotive incandescent lamps but there it is not reduced, and it functions well to absorb other impurities.  The patent states that in the neon flicker lamps, the coating is only partially decomposed.

Nitrogen is a strong discharge quencher and is usually avoided at all costs in discharge lamps.  If the coating were not at least partially decomposed, I don't think it would be possible to strike a discharge at all.  However the partial decomposition will solve that, leaving only a very tiny trace of azide and nitrogen present in the lamp.  So perhaps when the discharge strikes, it causes a local decomposition of the remaining azide which releases a small puff of nitrogen that blows out the discharge in that spot.
 The discharge would then be forced to migrate to another area, and by that time the nitrogen is re-absorbed by the getter / emissive coating.  As the patent states, by inclining the electrodes slightly such that the top spacing is wider than below, the general tendency is for the dicharge to move upwards and thereby resemble a candle flame.