You have posed the question so well that there's not much to be said in response, except: "Yeh, who knows?"

In physics, as in every day life, time is nothing more than the number of repetitions of an oscillator, or orbits and turnings of a planet, that accrue while an event is being "timed." That's it; there's no more to it than that! So much for our formal understanding. The concept of "verb," and particularly the verb "to be," seem to imply more than this, but if nothing happens, and nothing is there, what then?

I might add that relativity's view of time as a 4th dimension adds no insight; it just facilitates a neater formalizing of the mathematics.

Psi phenomena demonstrate how primitive our understanding still remains, in spite of our marvelous harnessing of what we do know in the form of gadgetry. We're great tool makers but poor philosophers.

Thanks for the recommendation. Your response has sharpened the focus enough here to pose the following question:

What triggers the sequences of states? In ordinary physical reality, it's spontaneous quantum jumps within a system, or interactions with other systems. But this just seems to place the notion of "time" one step further into the unfathomable, as the adjunct of physical law; and we have no idea where these "laws" come from. But maybe that's as far as we can go?

Ideas undoubtedly, at least in sentient beings, are associated with states in the brain. But what about psi phenomena? Perhaps we just need better formulations of physical law that allow "jumping around" processes within potential sequences? I'm not sure what meaning "potential" has here, but words fail me. That's why I like mathematics: one is severely limited in scope, but one can point at the result and challenge anyone to fault it.