I feel the Moon is associated with both the body and the mind, whilst the Sun lies closer to consciousness as such and identity. But there is overlap between the solar-lunar duality, and the two form a cosmic pair ruling the Earth as biological sovereigns over nature. The lunar body of the individual is psychosomatic, and is conceived of as a psychic body much more than a hypothetical solar body— but consciousness can solidify too, in a more abstract way. This must be due to the nature of the Moon itself, the corporeality which viscerally mirrors something for us which the Sun can't. The Moon as a corporeal, yet spiritual skeleton embodies the condition of birth and death, counterposed to the imperceivable Sun which is an eternal though still elusive, through this imperceptibility, essence.
This is why you can talk about a lunar body and why there must thus be a similar lunar terminator expanding and receding within our own psychosomatic body, and where differing elements of light and shadow coalesce with each other.
I don't think astrology intends to directly correspond the astronomical lunar phases with the psychological ones. The lunar tide constantly cycles in the rhythm of life, and it might be more useful to conceptualize an individual's lunar body as an inner moon which is merely the child, and not the slave of the Mother Moon.