The use of the word witness is not to imply what Brahman is. The use of the word witness is to imply what Brahman is not in relation to the world of maya - We can only say what Brahman is not, Brahman is without attributes; Brahman is not attached to this world. The use of the word witness is to convey the idea that we cannot know Brahman.
Brahman is described as Nirguna Brahman and Saguna Brahman (Iswara). The difference between these two terms/descriptions has been described in different questions and answers on this forum. Nirguna Brahman has no awareness of maya; Saguna Brahman does.
Brahma Sutras 2.3.46-47 (https://www.wisdomlib.org/hinduism/book/brahma-sutras/d/doc74896.html) says:
- The Supreme Lord is not (affected by pleasure and pain) like this (individual soul), even as light etc. (are not affected by the shape of the things they touch).
If the soul is a part of the Lord, the question may arise that the Lord also experiences pleasure and pain like the soul, even as a cloth is soiled if its threads are soiled. This Sutra refutes it and says that the Lord does not experience pleasure and pain like the soul, which on account of ignorance identifies itself with the body and mind, and thereby partakes of their pleasure and pain. Just as the light of the sun, which is all-pervading, becomes straight or bent by coming in contact with particular objects, or as the ether enclosed in a jar seems to move when the jar is moved, or as the sun appears to tremble when the water in which it is reflected trembles, but in reality none of them undergoes those changes, so also is the Lord not affected by pleasure and pain, which are experienced by that imagined part of it, the individual soul, which is a product of ignorance and is limited by the Buddhi etc.
- The Smritis also state (that).
“Of the two, the Supreme Self is said to be eternal and devoid of qualities. It is not touched by the fruits of actions any more than a lotus leaf is by water. . . Smriti texts like this declare that the Supreme Lord does not experience pleasure and pain. The Srutis too do the same.
And in his Pancadasi, Chapter VI, Sri Vidyaranya Swami says (Swami Swahananda translator):
As person with a special privilege, Isvara rules the universe. Without His rulership there would be no one to regulate bondage and release (Svetasvatara Up. 6.16-17)
The Sruti declares that Nature functions in fear of Iswara. He is the ruler though unattached. The rulership is appropriately vested in Isvara, who is not affected by sufferings, works, and so forth.
Vide Taittireya Up. 2.8.1, Katha Up. 2.3.3, Nrsimhatapaniya Up. 2. Rulership is not improper as Isvara is distinct from Jiva.
In his Vivekacudamani, Sankara says (Swami Madhavananda translator):
- The Supreme Self, different from the Prakriti and its modifications, of the essence of Pure Knowledge, and Absolute, directly manifests this entire gross and subtle universes in the waking and other states, as the substratum of the persistent sense of egotism, and manifests Itself as the Witness of the buddhi, the determinative facility. (Witness of the buddhi - All actions that we seem to be doing are really done by the buddhi, while the Self ever stands aloof, the only Absolute Entity.)
Your second statement as to what perception is makes many assumptions as to what constitutes perception - and is not necessarily a generally agreed as you state. There is an extensive review of what perception is in Advaita here under the section Diacritical Arguments For The Unreality of the World in the Chapter on Post-Shankara Vedanta - https://archive.org/details/IndianPhilosophyACriticalSurvey/mode/2up
Swami Vivekananda states (Complete Works, Volume 7, Inspired Talks, Wednesday, July 17, here - https://advaitaashrama.org/cw/):
Differentiae becomes qualities when they are separate but joined in one object. We cannot say positively what differentiation is. All that we see and feel about things is pure and simple existence, "isness". All else is in us. Being is the only positive proof we have of anything….
Shankara says again, perception is the last proof of existence. It is self-effulgent and self-conscious, because to go beyond the senses we should still need perception. Perception is independent of the senses, of all instruments, unconditioned. There can be no perception without consciousness; perception has self-luminosity, which in a lesser degree is called consciousness. Not one act of perception can be unconscious; in fact, consciousness is the nature of perception. Existence and perception are one thing, not two things joined together. That which needs no cause is infinite; so, as perception is the last proof of itself, it is eternal. It is always subjective; perception itself is its own perceiver. Perception is not in the mind, but perception brings mind. It is absolute, the only knower, so perception is really the Atman. Perception itself perceives, but the Atman cannot be a knower, because a "knower" becomes such by the action of knowledge; but, Shankara says, "This Atman is not I", because the consciousness "I am" (Aham) is not in the Atman. We are but the reflections of that Atman; and Atman and Brahman are one.
What you are thinking of perception is the perception of the waking state, the individual ego. Perceiving objects, memory (remembrance), are all in the waking state. The Consciousness, the perception of Brahman is the Turiya (Mandukya Upanishad). There are no objects to perceive, no past, no future. Just 'Isness'.
Krishna says in the Gita 9.4-5 (Swami Nikhilananda translator):
By Me, in My unmanifested form, are all things in this universe pervaded. All beings exist in Me, but I do not exist in them.
And yet the beings do not dwell in Me--this is My divine mystery. My Spirit, which is the support of all beings and the source of all things, does not dwell in them.