Gross and subtle ordinary appearances and conceptions can be understood from the side of the object and from the side of the mind realizing it.
Overcoming gross ordinary appearances essentially means a direct realization of emptiness in meditative equipoise on emptiness. At such times we perceive directly the mere absence of all the things we normally see. We have attained the first union of non-dual appearance and emptiness – the union of the appearance of clear light and its emptiness. We see the clear light as non-dual with its emptiness. We see the clear light as a manifestation of its emptiness. This is essentially the first profundity. From a sutra perspective, this is realized with a gross mind. From a tantra perspective, this is realized with our very subtle mind of great bliss. In Mirror of Dharma, VGL differentiates the union of non-dual clear light and emptiness and non-dual bliss and emptiness as two different examples of the union of appearance and emptiness. But it is still just the first profundity, just at a deeper level.
But to “complete the practice of clear light” we need to purify our obstructions to omniscience. Just as the conventional nature of the mind is so clear it can know objects, the clear light is to empty it can appear subtle conventional objects as non-dual with emptiness. In Eight Steps to Happiness, VGL explains that subtle conventional truths are not conventional truths, but ultimate truths. They are various things appearing directly as emptiness. An omniscient mind perceives “only emptiness” but it appears in myriad ways, of which the appearance of clear light is merely one. The non-dual appearance of myself as the deity, my car, my computer, my phone, Donald Trump, etc., are others. They are these various things appearing directly as emptiness or, from another angle, only emptiness appearing as various things.
In other words, to directly overcome subtle dualistic appearance – attain a realization of non-dual emptiness and subtle conventional truths (seeing subtle conventional truths directly as ultimate truths, only emptinesses), we need to train in the second, third, and fourth profundities, both in meditation and outside of meditation. We do it inside of meditation by meditating on non-dual profundity and clarity, for example with our self-generation meditation; and we do it outside of meditation by training in subsequent attainment, in particular according to the instructions of training in the meditation break explained in Tantric Grounds and Paths in the section on Isolated Body. This process of realizing the second, third, and fourth profundities itself occurs at two levels: at the level of our gross mind (Sutra) and at the level of our subtle and very subtle minds (Tantra).
I would also add even this explanation is not sufficient. We need to realize Nagarjuna’s intention according to the Ganden Oral Lineage. VGL explained this in his oral commentary to Mirror of Dharma and through the Gen-la’s in Arizona. The difference between the explanation from the perspective of the four profundities and from the perspective of Nagarjuna’s intention is we realize not only the union of appearance and emptiness (four profundities), but the union of karma and emptiness (Nagarjuna’s intention). We realize not just the union of appearance and emptiness, but the union of KARMIC appearance and emptiness. This is like the difference between realizing a static picture (four profundities of the non-dual Toyota and emptiness) and a dynamic karmic movie (seeing the Toyota driving down the street as the unfolding of karma inseparable from emptiness, seeing it as a manifestation of emptiness, seeing it as only emptiness appearing as a karmic unfolding appearing in this way). Realizing non-dual karma and emptiness is even deeper than the mere realization of non-dual appearance and emptiness of the four profundities according to highest yoga tantra. I think only when we realize non-dual karma and emptiness with our very subtle mind of great bliss do we actually remove the last traces of obstructions to omniscience and realize Nagarjuna’s (and Buddha’s) ultimate intention and attain full enlightenment.