let us understand how is He the consciousness of the conscious?

“There the sun does not shine, neither do the moon, and the stars;

nor do these flashes of lightning shine.

How can this fire?

He shining, all these shine;

through His lustre all these are variously illuminated.”

Shvetashvtara Upanishad[6:14]

Meaning:

There in the Supreme Self the sun though it is illuminator of everything does not shine, i.e. it does not revel Brahman. For the sun illumines all the forms through the light of Brahman indeed, who is the Self of all. In itself the sun has no power of illumination.

Few philosophical insights:

Tatra Surya na bhati:

There in the Supreme Self the sun though it is illuminator of everything does not shine, i.e. it does not revel Brahman. For the sun illumines all the forms through the light of Brahman indeed, who is the Self of all. In itself the sun has no power of illumination.

na chandra-tarakam:

Similarly, neither do the moon and the stars illumine the Brahman.

Na imah vidyutah bhanti :

neither do these flashes of lightening shine.

Kutah ayam agnih:

How can this fire that is known to us?

To be short: The fact that this world shines it is because

tam eva bhantam, anubhati sarvam:

He Himself shining, being effulgence by nature; it anubhati, shines accordingly- as for instance, hot-iron burn not by itself but when coming in contact with the fire does so. It takes the heat from the fire and burns. Actually heat of the fire burns but we say hot-iron burns.

Tasya Bhasa, sarvam idam vibhati:

Through His lustre alone; all these, sun etc. shine.

It has also been said, “Being illumined by whose light the sun shines” (Tai.Br. 3.12.9.7); “Neither the sun nor the moon or fire illumines That, that is My Supreme Abode, going whither they return not.” (Bhagavad Gita 15.6)

Incidence in the life of Mahapurush Maharaj, Swami Shivananda:

Once, very late at night, Mahapurush Maharaj and I were sitting together. No one else was there. A white cat entered the room through the southern door, and Mahapurush Maharaj began saluting it. As the cat meowed a few times and went out through the north door on the roof, Mahapurush Maharaj continued making his pranams to the cat. I kept wondering what it all meant. A little later, he said to me, ‘You see, Keshav, Thakur has kept me in such a state that I see everything pervaded by consciousness. Nothing exists but that.’ Then touching my body, he said, ‘You are consciousness. This cot is consciousness. The wall is consciousness. Everything else is consciousness. I am unable to control myself. Whenever the boys come in, I salute them first. Of course, I know it makes them feel bad, but what can I do? The Lord has now kept me in this condition.’

[as narrated by Swami Akshayananda, taken from Mahapurush Maharaj as we saw Him, page 234.]