Well, unlike a fundamental theory of physics, we don't have strong reasons to expect that consciousness is indescribable in any more basic terms. I think there's a confusion of levels here... GR is a description of how a 4-dimensional spacetime can function and precisely reproduces our observations of the universe. It doesn't describe how that spacetime was born into existence because that's an answer to a different question than the one Einstein was asking.

In the case of consciousness, there are many things we don't know, such as:

1: Can we rigorously draw a boundary around this concept of "consciousness" in concept-space in a way that captures all the features we think it should have, and still makes logical sense as a compact description

2: Can we use a compact description like that to distinguish empirically between systems that are and are not "conscious"

3: Can we use a theory of consciousness to design a mechanism that will have a conscious subjective experience

It's quite possible that answering 1 will make 2 obvious, and if the answer to 2 is "yes", then it's likely that it will make 3 a matter of engineering. It seems likely that a theory of consciousness will be built on top of the more well-understood knowledge base of computer science, and so it should be describable in basic terms if it's not a completely incoherent concept. And if it is a completely incoherent concept, then we should expect an answer instead from cognitive science to tell us why humans generally seem to feel strongly that consciousness is a coherent concept, even though it actually is not.

OTOH, if there isn't some other theory that explain consciousness in terms of more fundamentall entities, properties, etc, then reductionism is out of the window...and what is left of physicalism without reductionism?