The reason that you don't see a lot of dialogue about time is that it is a difficult subject to get right at the best of times, and not really necessary to liberation. It might be considered nothing more than a cosmological inquiry, something to be avoided in favor of practice. However...
All that which is compounded, conditioned, dependently arisen and empty is impermanent, temporary, an apparition, ephemeral, gone already, in fact never here at all. Time is empty, it is conditioned, compounded, ultimately unreal. It cannot be truly grasped. Nagarjuna tackles time in chapter 19 of his Mulamadyamakakarika, aka the Fundamental Wisdom of the Middle Way.
He begins with a demonstration that it is absurd to postulate the true existence of an actual past, present and future, asserting that these things exist in name only, as concepts only. The arguments he makes here are complicated, rely on previous chapters of his book, and concern causality, interdependence and the nature of how things arise, and the full argument is beyond the scope of a comment thread. Essentially, however, an existence with a true past, future, and present moment that actually exist is seen as a mere concept, and is therefore unreal. Common sense time is unreal. This realized wisdom has the effect of releasing us from the anxiety of the pressing urgency of time.
Since time as past, present, and future is ultimately unreal, we move on to time as a fleeting flow vs time as something that can exist in "a singular moment" of time. This is also demonstrated to be lacking of true existence. Continuously fleeting time cannot be grasped, and if a moment of time is singled out, it ceases to "be" time. Time is ungraspable. This realized wisdom has the effect of releasing us from grasping and clinging at time.
Finally, he argues against a self-existing time, showing time as being compounded. In his study on the Mulamadyamakakarika Jay Garfield concludes that
Nagarjuna points out that with no entities to be temporally related,
there is no time. That is, the only mode of existence that time has is
as a set of relations among empirical phenomena. Apart from
those phenomena and those relations, there is no time. But that
means that, given the lack of inherent existence of phenomena,
there can be no inherent existence of time. Time is thus merely a
dependent set of relations, not an entity in its own right, and
certainly not the inherently existent vessel of existence it might
appear to be.
Emphasis added was mine, as it pertains directly to your question. The effect of this realized wisdom is to release us from the erroneous notion of an absolute, true existence of time, this eases grasping at true existence. It shows us that time is relational, is tied to space and objects, and that since no true objects have absolute existence, neither does time. It is just another phenomena in flux.
A study of this chapter can be found here, with an emphasis that what Nagarjuna denies is absolute time, or an independently existing time.
Nagarjuna, a founder of Middle Way, Mahayana philosophy, shows us that the only way to consider time is as empty, relative time that is dependent on other phenomena to exist at all, and, like all other phenomena, is always in flux. It conventionally is a co-dependently arisen phenomena, and therefore ultimately is unreal, that is to say cannot be truly found when looked for. This is how time is actually experienced. Unreal, ungraspable, empty.
Finally, impermanence is not, in any way, a thing that is housed. It is a characteristic of all phenomena. To say that it is housed is erroneous, the apparent objects that are marked by impermanence are not even seen as having self-existence, so no true object at the end of the day outside of the concept of one. So there is, ultimately, no object to hold the characteristic, only the perception of non-permanence.