Recalling Neither Perception nor Non-Perception for Nimittas

I would also say that it is largely irrelevant, given the keywords you’ve listed as constraints for your requested answer. However, I would like to make a correction to the phrasing of your question in that it is not “the ability to discern and cognize... that are absent” but discernment and cognition that are absent, i.e., the faculty is there, but quiescent. It isn’t a meaningless difference, and is important in tantrayana practices.

In practice, this is a state in which there is just spaciousness. No thought of a meditator meditating, or of accomplishment, enlightenment, wisdom, perfection, nor anything else. No thoughts arise. Sensations are no longer attended to, not because one stops attending to them, but because that discriminating response is simply no longer functioning. If you turn your mind toward such a sensation, it will be actively apperceived as a sensation of a particular type, so the mind must rest as it is: spaciousness—but not just empty dead space. Instead, one reaches a stage where there is just clear lucidity, in the sense of reflexive knowing that we can also call clarity. This means our normal perspective evaporates. Time no longer passes. There is not even a need for the concept of "now." Just illumination without limit. Beyond this, there can be only poetry.

As Jigme Lingpa, ending with a quote from the “Perfected Skill of the Lion” tantra, puts it:

Thus, according to the tradition of this vehicle, the nature of the mind is—from the very beginning—great natural liberation. Recognizing that is called “awareness.” By maintaining this continuity, the state of Buddhahood will be directly realized, which is why this path is more expeditious than any other. In this way [practitioners] will gain inspiration.



In addition, [the instructions] on clarifying doubt and subduing hinderances are as follows. While maintaining the continuity of the great, indwelling fundamental nature, if one thinks that the nature of this awareness is empty, the one ascribing emptiness to this is the intellect, which has a focal point. The way the meditative concentration with a focal point does not produce Buddhahood is as stated in the “Perfected Skill of the Lion” tantra:



“The meaning of the nature of phenomena cannot be seen through meditation with concentration. The samādhi of one’s own appearances eludes the direction of concentration. Free from elaboration, the nature of phenomena is equal to the limits of space. All mental considerations are devoid of conceptual fixation with objects. The dharmakāya Buddha free from the four extremes, such as existing or not, is one's own awareness” (“The Yeshe Lama,” page 5)

I'd argue that its largely irrelevant. The content of meditative experience really has no bearing on ones practice. The insight that is attained when one emerges from those states is what matters. The only value of truly deep meditative absorption is that it allows for equally deep vipassana.

The sutta is peculiar

Sariputta entered & remained in the dimension of neither perception nor non-perception. He emerged mindfully from that attainment. On emerging mindfully from that attainment, he regarded the past qualities that had ceased & changed: 'So this is how these qualities, not having been, come into play. Having been, they vanish.' He remained unattracted & unrepelled with regard to those qualities, independent, detached, released, dissociated, with an awareness rid of barriers. He discerned that 'There is a further escape,' and pursuing it there really was for him.

Qualities here is 'dhammā', plural hence the 'ā'

The sutta is peculiar because it does not say what those dhammā are as it does for the other attainmemts as in;

Whatever qualities there are in the dimension of nothingness — the perception of the dimension of nothingness, singleness of mind, contact, feeling, perception, intention, consciousness, desire, decision, persistence, mindfulness, equanimity, & attention — he ferreted them out one after another. Known to him they arose, known to him they remained, known to him they subsided. He discerned, 'So this is how these qualities, not having been, come into play. Having been, they vanish.' He remained unattracted & unrepelled with regard to those qualities, independent, detached, released, dissociated, with an awareness rid of barriers.

This sutta simply doesn't say what those qualities are in the case of neither perception nor non-perception and the expression is reduced to

So this is how these qualities, not having been, come into play.

I can only speculate as to why the naming of the dhammā is omitted but the point is that there are dhammā which can be ferreted out one-by-one & named and dispassion towards those dhammā ought to be developed.

The property of the dimension of neither perception nor non-perception is to be reached as a remnant-of-fabrications [sankharā] attainment.

BTW;

As for these two dimensions — the attainment of the dimension of neither perception nor non-perception & the attainment of the cessation of feeling & perception — I tell you that they are to be rightly explained by those monks who are meditators, skilled in attaining, skilled in attaining & emerging, who have attained & emerged in dependence on them.”