There are some possibilities here.
1: You live in a house where somehow, weirdly, the power dips and unbalances when there is no use. That normally only happens with over-use, though.
2: You're like every single other person in the world and have working pupils and a normal human brain. (That may either be a relief to you, or a shock, I hope the prior).
Of course, there are some other options, but I'll explain the more likely number 2.
Step one to that is that our brains are amazing processors that know what is important and what is not in the context that they are seeing. We've trained them for millions of years to become good at that. So in normal conditions the flickering is unimportant and boring to your brain.
Step two is that in low light conditions your pupils widen, allowing a lot more of the light and differences into our eyes. Presenting, suddenly, a much stronger flicker to your brain in a dark environment with nothing else to process.
Step three is that your brain is also very good at fooling itself; you see what you think you see. If you start focusing on the Light your expectations exaggerate the actual flickering.
Step four is that any light source will create a huge amount of light compared to the Neon light, closing your pupils, removing the level of detail from the Neon light and also adding a lot of new information for your brain to focus on that seems more important. (Where the chairs are. Are there any feral cats under my desk? Did you get any new texts? Why has {insert cute girl [-or boy as far as I care-]'s name here} not responded yet?)
Step five is an actual thing that happens: The light turning off can happen once in a while through either the light wearing down, or having small moments of high levels of polarization in a place where there's little fluorescent material, so that all current flows there for a second or two creating nearly no light. This would logically also happen when the lights are on, but you may just not notice so much with a lot of light around you, since the event is not significant at all. Think about it: If you have 5000 Neon lights, and one pops off, how long would it take you to notice? If you have only one of those same lights, and it goes off suddenly, you're bound to see immediately: All your light is gone!
The fifth is helped by the Neon lights in power strips costing a negligible amount of money, as they are the cheapest kind of Neon light ever invented. 'You get the quality you pay for'.
All that said, of course, there may be a combination of several things going on. But I'm betting (heavily) on the flickering/no-flickering definitely just being a change in perception.
The Neon's in series with a load, such as in a wall light switch, can of course exhibit all kinds of strange behavior with capacitive loads, or inductive loads, or very light loads. But the Neon in a power strip is directly connected to the mains through the switch, in parallel with all other loads, so that's not happening here.
It might only 'spark a bit brighter or dimmer' just the once when you switch on or off a very heavy load, but that should be clear enough, in some buildings all the lights always do that.