Are there any arguments about qualia that are analogous to those about cause?
I would be surprised if there was any.
The term "qualia" was coined specifically to identify what was potentially specific to our subjective experience, namely that it is the experience of qualities, the painful quality of pain, the kaleidoscopic qualities of colours, the myriad of impressions often too elusive to otherwise describe.
Qualia are thought of as specific to subjective experience but a subject may not recognise qualia as qualia. The expression "naive realism" elicits the default mental mode whereby qualia make up the experience we have of the world and all but disappear in the process as qualia. What is left is the world as we experience it. In other words, oblivious of qualia, we mistake them for the real world around us.
The main difference between qualia and our everyday as well as scientific conception of the physical world is that qualia don't come with quantities attached to them. By contrast, we think of the physical world, again in both our everyday and our scientific perspectives, as quantities of properties defined over space-time.
Causation then is a relation between some such quantities at a particular point in space-time and some such quantities at another particular point in space-time.
We attach quantities to physical properties just because we can. The physical world, at least as it appears to us, lends itself to being measured. Once we can measure the quantities attached to various properties, we can work out the deterministic way that these quantities will evolve over space-time, giving rise to our notion of causality.
Qualia, assuming that we recognised them as such to begin with, have no quantities attached to them beyond absence and presence. We take qualia to be somehow a consequence of the physical world. This is inevitable since the physical world appears to us as qualia and only as qualia. Indeed, we came up with a specific word to talk about qualia as qualia only fairly recently in our history. It was Clarence Irving Lewis who first used the word "qualia" in the philosophical sense it is used today. That was in 1929:
There are recognizable qualitative characters of the given, which may be repeated in different experiences, and are thus a sort of universals; I call these "qualia." But although such qualia are universals, in the sense of being recognized from one to another experience, they must be distinguished from the properties of objects. Confusion of these two is characteristic of many historical conceptions, as well as of current essence-theories. The quale is directly intuited, given, and is not the subject of any possible error because it is purely subjective. - Clarence Irving Lewis, in his book Mind and the World Order (1929)
We thus usually accept, essentially implicitly, as if by default, that qualia come and go not because of some causal relation between them but as a result of what happens in the physical world, somewhat like shadows move according to how material things move rather than because of some ontological property of the shadows in themselves.
There is of course no scientific theory as to precisely how qualia come and go. Qualia are not even thought of as susceptible to being scientifically investigated. Thus, qualia are very nearly thought of as epiphenomena:
Epiphenomena - A secondary phenomenon that results from and accompanies another.
Thought of as epiphenomena, but never explicitly theorised as such.
There seems to be two different reasons for that. First, qualia are not even recognised by the scientific community as physical. Indeed, they are barely acknowledged as real. Many scientists would rather say that they have the status of subjective illusions. And you cannot investigate the physical cause of non-physical beings.
Second reason, even if properly acknowledged, qualia are eminently subjective by definition and science doesn't investigate the subjective except through objective proxies, when proxies exist, and none have been identified for qualia yet.
There is also the special role of qualia. Qualia are what we know and we know nothing but qualia. The material world is represented in our consciousness as qualia. The entirety of our physical model of the material world is an abstraction. Thus, the possible causal relationship between qualia and the physical can only appear to us as a very confused question:
How do you model the way that what the model represents somehow causes the model, and causes the model to be what it is, and causes the model to represent what it represents etc.?
This might very much be a hard problem.