Consciousness has to be existent, otherwise how will ere it be there? But is existence consciousness or not or not? And it does not seem to be. There are many things which seem to exist and they are not conscious. In fact, if you go further, the only thing of which you have direct evidence of consciousness is you,. Everybody else.
Inspired by the 15th chapter of the Ashtavakra Gita, Swami Sarvapriyananda gives a discourse on the nature of the Self.