jyotiṣām api tajjyotiḥ tamasaḥ param ucyate | jñānaṁ jñeyaṁ jñānagamyaṁ hṛdi sarvasya viṣṭhitam ||13.17||
That (jñeyaṁ brahman), the light of lights, is said to be beyond ignorance. It is knowledge, it is that which has to be known, it is that which is arrived at by knowledge and it is present in the minds of all.
Just how usually we look at any creation in this transactional world, the material cause is separated from the maker/intelligent cause. But brahman is presented as material cause as well as intelligent cause of the universe. The nature of sat - existence is the basis to sustain all the names and forms (as material cause) and in the same time the nature of cit - consciousness is the knowledge of all creation (as intelligent cause). Sat and cit are not two different nature of brahman which being explained differently due the point of view. The existence we talked about is consciousness / knowledge alone, since there is no creation possible without knowledge and knowledge is not possible without an existence entity. And this establishment only can be done by consciousness. Just like dream, my entire dream world is nothing but my knowledge, the material cause and intelligent cause are nothing but one consciousness. And I the consciousness is the one who prove the existence of my dream.
Lets us try to understand cit from the total level. When we see a piece of stone before being carved into a mūrti (statue), the existence and the knowledge (how the mūrti looks like) is pretty much there in the stone, but only manifested after the touch of the sculptor. The knowledge is not from the sculptor then later on transferred to the stone, in fact the sculptor is the one who can see the knowledge in the form of figure in the stone, then bring it to the manifest form. The knowledge is in and through the entire statue supporting the entire looks of the statue after being carved (knowledge of the figure of particular deity is there). And even when the figure is destroyed, knowledge of a figureless statue is there. In the example, knowledge of the certain form of deity comes and goes, it is called attributed knowledge - viśeṣa-jñānam. But there is unqualified knowledge -samanya-jñānam which is the base for the arrival and departure of attributed knowledge. There is no creation possible without knowledge, and any given knowledge is not there without consciousness, thus there is no creation possible without consciousness. And who is that consciousness?
When a pot is seen, that means knowledge of the pot exists. Because anything has to be cognised then we can call it as knowledge. I the consciousness become the knower of the pot when a qualified knowledge called pot is cognised by me. In this process, knowing happened which we usually called as knowledge. This triad of knower-known-knowledge arises together and goes together. Because when the qualified knowledge called pot is gone, the knower of the pot is also gone, and cognition of the pot is gone at the same time. At this time, when the qualified knower of the pot, qualified known pot and qualified knowledge of the pot are gone, what is left? Only one unqualified knowledge/consciousness remains. This consciousness (unqualified knowledge) - samanya-jñānam is there all the time to witness the arrival and departure of any attributed knowledge - viśeṣa-jñānam (knower of pot, known pot and cognition of pot). Every qualified knowledge needs to have its basis on the samanya-jñānam - unqualified knowledge which is consciousness. Just like when you see a pot, the knowledge/ consciousness of the pot "is", then I take away the pot, and show you a cloth. Now the knowledge of the pot "is not", but knowledge of the cloth "is". But in between knowledge of pot and knowledge of the cloth, consciousness still "is" without any attribute. This is the samanya-jñānam which can never be negated in all period of time and it is there in cognition of all names and forms. In any cognition, there are always samanya-jñānam and viśeṣa-jñānam together, because without consciousness, there is no thought can be objectified.
Doubt: you say existence of any given thing can be proved only by consciousness, but we can't say any given thing is not exist without my or anybody's cognition. Answer: yes it is true, its existence is not proven by attributed consciousness as me or you, but it is proven by consciousness/knowledge which is the basis for that entity to exist, because consciousness is self-evident.
Therefore to ascertain the existence of any name and form, we need consciousness to do that, because the nature of consciousness is always illumine, makes names and forms come to being. But to ascertain consciousness, only the self-conscious being which exists can prove consciousness itself, because it is being self-evident. Without consciousness there is no attributed pot consciousness, cloth consciousness, etc. Thus consciousness exists in any transaction in the form of knower-known-knowledge. They seem to be three different things, but in reality they are only one consciousness which is being attributed. Just like the entire dream where there are dreamer (one who sees the dream), individuals dream's characters which get their own minds and transaction between them. But the dreamer, dream objects and the dream are nothing but knowledge of one conscious entity. When this entity wakes up from identification with the dream, then the dreamer, dream objects and dream itself are resolved back to the very same person who has nothing to do with them.
Therefore Lord Krsna says consciousness brahman is light of the lights - jyotiṣām api tajjyotiḥ. Light is that by which we can perceive things visually, makes things become evident to us. But if we choose to close our eyes, is the thing which lightened by light still come to our perception? No, In this case our eyes become that which light up the object, make it evident. But if the mind is not there, nothing can be seen also. And mind itself need to be backed up by consciousness, otherwise it is also a non sentient things which couldn't perceive anything. Thus the ultimate seer who proves the existence of others in the same time proves its own existence is consciousness - me alone.