I think in these sort of topics we are often discussing two different meanings of consciousness: physical vs philosophical. The arbitrary mixing and matching of them is likely one the reasons for the lack of clarity. Physical consciousness is most easily identified by the notion that you're unconscious when sleeping. The other is the far more interesting philosophical consciousness.
Philosophical consciousness is what the oft misunderstood quote cogito ergo sum, I think therefore I am, was hitting on. Descartes was not saying that consciousness is defined by thinking. He was trying to identify what he could know was really real in this world. When one goes to sleep, the dreams we have can often be indistinguishable from a reality in themselves, until we awake and find it was all just a dream. So what makes one think this reality isn't simply one quite long and vivid dream from which we may one day awake?
But this wasn't an appeal to nihilism, the exact opposite. The one thing he could be certain of is that he, or some entity within him, was observing everything. And so, at the minimum, this entity must exist. And the presence of this entity is what I think many of us are discussing when we speak of consciousness. In contrast to physical consciousness, you are philosophically conscious even when sleeping.
Of course like you said philosophical consciousness cannot be proven or measured and likely never will be able to be, which makes it an entirely philosophical topic. It is impossible for me to prove I am conscious to you, or vice versa, no matter what either of us does. Quite the private affair, though infinitely interesting to ponder.