I'm looking specifically for meditation instructions applying the mentioned method and pointing out that not finding anything as the essence of mind, or mind itself is the whole point.
Something similar can be found in this classic Zen story, but even this is not exactly it:
Bodhidharma sat facing the wall. The Second Patriarch stood in the snow. He cut off his arm and presented it to Bodhidharma, crying, "My mind has no peace as yet! I beg you, master, please pacify my mind!" "Bring your mind here and I will pacify it for you," replied Bodhidharma. "I have searched for my mind, and I cannot take hold of it," said the Second Patriarch. "Now your mind is pacified," said Bodhidharma. (Gateless Gate, case 41, tr. by Katsuki Sekida)
Also a passage that comes close to it from the MPPU (chapter on the Mahayana form of smrtyupasthana, mindfulness of mind):
"And although the wise person considers the characteristics of birth (utpāda) and cessation (nirodha) of this mind, he will find no true birth, no true cessation. Not finding any defilement (saṃkleśa) or purification (vyāvadan) in it, he discovers this luminosity of the mind (cittasya prabhāsvara), a luminosity by virtue of which the mind is not defiled by the adventitious passions (na khale āgantukair upakleśair upakliṣyate)." (tr. by Gelongma Karma Migme Chodron of Lamotte's translation, vol. 3, p. 979 / PDF p. 118)
What I'm looking for actually fits the "emptiness of non-perception":
何以故名不可得空？為智力少故不可得？為實無故不可得？ 答曰： 諸法實無故不可得，非智力少也。 (T25n1509_p0295c13)
"Why do you assert this emptiness of non-perception? If dharmas are not perceived, is this due to weakness of knowledge (jñānadaurbalya) or because they do not truly exist?
Answer. – It is because dharmas really do not exist that they are not perceived, and not due to weakness of knowledge." (vol. 4, p. 1762 / PDF p. 358)
However, the 18 emptinesses are used more as theoretical teachings rather than practical ones.
"What is unascertainable emptiness? Those dharmas which are past, future, and present, are not got at. And why? In a past (dharma) the future (dharmas) cannot be got at: nor in a future the past; nor in a present (dharma) can the past and future (dharmas) be got at: nor in the past and future (dharmas) the present ones. The unascertainable emptiness is the non-apprehension of these, because they are pure from the very beginning, on account of their being neither unmoved nor destroyed. For such is their essential nature." (Large PP Sutra, I. 9, 12, §15. PDF p. 184)
"As soon as this present moment appears, at that very moment it will exhaust or cease to exist. The past is gone; the future has not yet come, so they are not entities. This is what we call ‘not apprehended’. But there is no such phenomenon about which you can conclude that it is an unapprehended phenomenon, because ‘unapprehended’ itself is empty. This is ‘emptiness of unapprehended’." (Dzongsar Khyentse Rinpoche's commentary to Madhyamakavatara 6:216-217 in "Introduction to the Middle Way", PDF p. 334)
It is not exactly like how Thrangu Rinpoche puts it:
"it has been resolved that objects of mind and mind itself are not to be found, and that the not-finding-anything when you look for the mind is not because you have failed to find it; nor is it because the mind exists but is somehow too subtle to be found in that way; nor is it because it is too far away from you, too distant to be seen after all it is your mind. The reason that you do not find anything is that in not finding anything you are finding what the mind is, which is emptiness, and this is a matter of direct experience." (Ocean of Definitive Meaning, p. 75)
"While teachers of the middle way, mind only, transcendent wisdom, mantra, and other schools may have their own assertions, the fulfillment of those intentions is the same. There is not a single thing that is not contained within mind."
(Gampopa to Düsum Khyenpa, in "The First Karmapa", KTD Pub, p254)
“If you recognize the world of appearance and existence as the mind, realize the mind itself as empty, and have no grasping at the superiority of your realizations — this is the ultimate view."
(Chegom Dzongpa, in "The Book of Kadam", Wisdom Pub, p609)