Agreed that core consciousness is pretty much static, but extended consciousness relies on memories, learning, sensory data, and emotions and therefore changes constantly. Core consciousness "provides the organism with a sense of self about one moment - now - and about one place - here" and is generated by basic brain structures including brainstem nuclei, hypothalamus, and somatosensory cortices.
Extended consciousness "provides the organism with an elaborate sense of self - an identity and a person, - and places that person at a point in individual historical time, richly aware of the lived past and of the anticipated future and keenly cognizant of the world beside it," and involves networks in the temporal and frontal cortices, subcortical nuclei such as those in the amygdala, coordination by the thalamic nuclei, and working memory in the prefrontal cortices as well. Core consciousness is possible without extended consciousness, but not vice versa.
"In short, core consciousness is a simple, biological phenonenon; it has one single level of organization; and it is not dependent on conventional memory, working memory, reasoning, or language. On the other hand, extended consciousness is a complex biological phenomenon; it has several levels of organization; and it evolves across the lifetime of the organism. Although I believe extended consciousness is also present in some nonhumans, at simple levels, it only attains its highest reaches in humans. It depends on conventional memory and working memory. When it attains its human peak, it is also enhanced by language." Quotes are from Antonio Damasio.