I have seen this similar EOL neon sign. I saw your youtube posting at the LG last night. It seems to be no difference between the 50 Hz and 60 Hz for the EOL behavior.

Now, I don't know if this is Neon tube is going bad or the step-up transformer going bad

I also don't know.
Since most of our local made neon signs, don't flickering, this means that they operating at high frequency, and this means that their NSTs are electronic.
These should have EOL protection.
But i think that the problem is with the neon sign itself, as the only problem that cause flashing of fluorescent lamps in HF gears, is a failure of the electrolytic capacitor (If it exist there), which results with a regular 50/60hz flickering.
Another evidence that they are operates at HF, is that i saw in the past, several neon signs with standing waves in the discharge.

Flickering is mostly caused by poor contacts, or a dying HV transformer. Another cause is if the glass has been coated by something conductive, like an accumulation of glass cleaner that builds up a slightly conductive film especially in a humid area. Rain has the same effect, but with a magnetic transformer it will stop when the glass dries off, along with the socket ends and insulators.

I don't know if the NSTs we have on neon signs, are also local made, but since this problem usually appears as a premature failure, you probably right.

I have 2 neon sign transformers that are new magnetic units, but the signs at work have older transformers that have been in service for close to 20 years, running off a selection of flashers ( that die at around the 5 year mark generally) where the maintainers have only changed one out that burnt off the connection on the insulator recently. They are pretty reliable, but do not like rain, it makes them flicker. Generally I get Claude Neon to clean them and repaint the masking every year, this helps a lot. The panel backlighting is done with 4 foot T8 tubes, and i supply those ( otherwise I would have assorted colour tubes in there depending what is on the maintenance truck) and new starters generally every 2-3 years. Phillips tubes last very well on 24/7/365.