In the mind moments before they cease. And in the new ones when they arise again.
In the physical body. There are materiality caused by consciousness and kamma, these are not accessible by our science, thus science doesn’t know these.
I see your misunderstanding now. Consciousness used in Buddhism doesn’t just refer to the state of being awake. It includes what modern psychology call the unconscious, and subconscious, it only disappears in the Brahma realm of unconscious, where there’s no mind, the cessation of perception and feeling, and parinibbāna. It is understandable that people can take this consciousness (what you call mind) to be eternal as long as their disappearance is not “experienced”. As there’s basically no was for an unenlightened person to know it as a human to disappear, except by seeing Nibbāna, one can know it is gone in parinibbāna.
I recommend you just read even a basic beginner’s book on Abhidhamma before trying to misrepresent it.
Abhidhamma divided the 4 aggregates of mind into viññāṇa (sutta) = citta (Abhidhamma), best translated as consciousness for viññāṇa or mind for citta. And feeling, perception and volitional formations are grouped under cetasika.
In the citta of Abhidhamma, as mentioned above, includes the sleeping mind, which is bhavaṅga, it’s nothing profound here, in meditation we are not encouraged to go into bhavaṅga as it’s just sleeping in meditation.
If your claim for Nibbāna without remainder is eternal bhavaṅga (since there’s no active sense base receiving objects), it’s just basically endless sleeping. Not a very profound or inspiring thing.
Whatever is citta, they are all conditioned, impemanent, subject to change. To sense things, the bhavaṅga mind has to cease for cognitive process to happen. Then the mind falls back into bhavaṅga and so on. It is impermanent. What’s impermanent cannot be clung to as safety, or unconditioned.