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Imagine an event of one second in length, like the blink of an eye. Suppose that another second elapses between the closing and reopening of your eyes, a second in which nothing happens in the whole universe (or in all universes). You and your eyelids stand still, and nothing else moves or changes, neither here nor anywhere - not a hair, a planet or a god, an absolute stasis. Does this second really pass?

If so, you could extend this second to a minute, a day, or a million years, because if nothing happens in this time interval, you can't determine how long it will last: an infinite time lurks between each instant. Time, therefore, seems not to exist unrelated to the relationships between things, because in a universe(s) without events it loses any value. Whatever the measure of an instant, in fact, it is such only in relation to some change: the rising of the sun, the motion of a hand, the appearance of a wrinkle, the resonance of an atom.

Does the minimum unit of time coincide with the smallest change? Does time dissolve without differences between things?

You already seem to know the scientific perspective on this, but perhaps it's still worth elaborating a bit on it.

You can define a second as the amount of time that passes between two ticks of the second hand of a clock. Our modern definition of the second is essentially a more precise version of the same idea, where the oscillations of the radiation emitted by a suitable atom play the role of the hand of the clock:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

So if nothing happens during your "second" in the whole universe—if no clock moves its hand and no electromagnetic wave oscillates—then no time has passed.

From a theoretical point of view, this hand of the clock or radiation does not necessarily itself need to be "real". It's enough to consider what would happen if such a clock or such radiation was present. An empty universe which contains no matter at all but in which times passes is perfectly conceivable by the laws of physics. Plain Minkowski spacetime is like that.

Since one might say that one of the important properties of time is to allow for change; to then suppose time exists, but that there is no change, rather goes against this.

It's a logical possibility, but then so is a universe with nothing in it; or indeed, no universe at all.

You seem to be asking "what is time?".

If you are asking in the sense of our science of physics, then time is defined by its measurement: time is what a clock reads. Quite literally that. And since Einstein, that is a rather flexible definition. Anyways, it does not tell you anything about what time actually is. But by that definition, in your example, since the clock itself would freeze for a minute or million years as well, your "pause" it would indeed not be relevant, and time (sic) would not progress until the clock continued moving.

If you are asking in the sense of "reality", then the answer is "nobody knows". We don't know enough about the universe to decide what things actually, really, really are, and physics does not change that in the least. This is not only true for time, but for anything at all. We only have mathematic/physical theories, which happen to not having been proven wrong yet, but all they do is make predictions about how certain measurements could turn out in certain experiments (our eyes are only measuring instruments as well). We arguably can never leave Plato's Cave, or at least we are quite far away from it.

If you asking in a philosophical sense, then the answer is up to you, really, to go by taste and opinion. People have come up with plenty of different interpretations.

Intuitively speaking, I find it hard for there to be time on the lapse you get at with the description, because the being that is that lapse lacks of numerous properties of time. For example, it lacks temporal asymmetry between events (any event occur at all), etc.

I am deducing this from Aristotle's interpretation of time in his Physics IV 10-14, where basically his strong claim is that time is composed of points that we mark in changes (as if we could represent changes in a line of real numbers, with a present (or now as he calls it) being a point in the line):

"when... the soul says the nows are two, the one before and the other after, then it is and this it is that we say is time" Physics (219a27-9).

For Aristotle, we know that time passes when we perceive two parts of a change, where an asymmetrical relation holds between them (one before the other), which we (our soul) mark as two nows with the correspondent temporal asymmetry (one before the other).

Therefore, if no change is contained in the lapse, no possible change part is in the lapse. This means there is no asymmetrical relation between parts that could possibly mark a correspondent relation between nows, that would mark the passing of time.

Another way to pose the same question might be to imagine that this universe we experience is in fact a computer simulation. Some rich kid outside this universe has been playing SimUniverse on the home computer. When the rich kid's mum calls him/her/it for dinner s/h/it presses the pause button. Nothing happens in our universe until s/h/it un-pauses. Has any time actually passed? Would any of us notice?

I think the answer depends on whether you are inside the simulation or outside it. From our perspective inside the simulation there is no change and no time passes.