Epiphenomenalists believe that consciousness exists but has no effect on the physical world. Why do they believe that consciousness exists? It would be a phenomenon completely unlike anything else in the world, but since it has no effect on the physical world there cannot be any evidence of its existence. How do they justify the existence of such a singular phenomenon without any evidence for it?
At the risk of pursuing peace when all sides want war, you need some sense of what you mean by a cause. Many things have multiple causes, but in some sense you have to choose a cause to be the 'most concrete' cause in a given circumstance. You need to choose a relevant point of leverage for language, or all such distinctions become circular.
Consider thermodynamics. We can look at it in many ways. We can think of it as being about heat as a force, or about temperature as a measure, or about the distribution of 'microstates', or as the side-effects of the molecular motion that cannot be fully described. Each perspective focusses on the notion of cause differently.
You can choose one of these and declare all the others wrong, or you can admit they all amount to the same thing. If you take the view that separates them, you quickly descend into absolute nonsense. This is the path that theory of mind seems to want to take. They all want to choose one of several basically equivalent viewpoints and create bizarre word games to claim the alternatives are not equivalent, for reasons of historical pride.
If we look at the versions of thermodynamics, we can map them vaguely onto theories of mind
"Heat as a Force", maps onto a straight functionalism -- we are concerned with effects and making engineering work, and we see inputs as causes, ignoring the detail that allows the energy transfer to take place. We see this interpretation just fails to give us any reasonable grasp of where some of the heat goes, but that is just life. The force of heat is the idealization of heat energy into a causal force.
"Microstates" maps onto emergentism -- we don't want to delve into what causes statistical variations in the distribution of energy, even though we need to look at it as energy and deal with the distribution of that energy as it is transformed back and forth from this form to and from kinetic and other stored forms. We have just enough handle to do the math right in our engineering, and we stop there. Microstates are the mechanism of emergence of heat energy, with entropy and information as other potential 'multiple realizations'.
Molecular motion maps onto materialism -- we see how the more complex phenomenon might be reduced to a more concrete observed phenomenon, and we are willing to believe it is totally explained by that more basic physics -- even though we can't do the math in most cases. So there is a bit more faith here than we might really be comfortable with. Molecular motion is the systematic reduction of heat energy to simpler physics.
That leaves the "transmission of temperature" model to map onto epiphenomenalism -- we know that temperature represents the quantity of something, and that if we trace the temperature as it travels, we can account for most of what is going on. But we also know that temperature is not causal, it is not a force, just the trace of one. Temperature is the basic epiphenomenon of heat energy.
We can agree that it does not cause anything, but is always and everywhere an effect of some cause we don't want to trace any deeper. It has no effect, it only accompanies effects.
Temperature then behaves quite like the thing you complain is 'singular'. Making neither of them 'a phenomenon completely unlike anything else in the world'. (Especially since any good science teacher can probably do this same breakdown for four or five rather old domains from electricity to acidity that have gone through a succession of equivalent models, and these same four stable positions are easy to identify in finance and psychology, as well.)
So there is no element of 'singularity' or other awkwardness involved.
We know that consciousness traces causal activity, as temperature traces whatever you want to describe heat via.
Consciousness is there when there is a mental cause, but we don't see how it can be the cause itself, because it does not seem to be structured in a way that other causes in our world are. This is very much the same way temperature is a very clear indication that traces when heat effects occur, but is not very directly converted into any field or kinetic measure that reliably works with the rest of physics.
Chalmers calls this The Paradox of Phenomenal Judgment and discusses it in chapter 5 of The Conscious Mind.
In essence, Chalmers believes roughly that indeed zombie-chalmers without that mysterious epiphenomena will report having it just as the real Chalmers, but will not be justified in doing so. Chalmers would say that "I know I have qualia and I know that I am justified in saying so", and he is aware that his zombie twin will say the same thing, but believes that the zombie will not be justified in saying so, and he is aware that the zombie would hold these exact same beliefs.
Eliezer Yudkowsky looks into Chalmers' explanation in an interesting article in Less Wrong.
I think there is no resolution to this paradox, and that at some level epiphenomenalists know it. In a way they are saying - reality is weird beyond our ability to make sense of it - and they are simply choosing to live with what they see as the least evil. They subscribe to living with that paradox as one subscribes to living without a leg, or a lung or a kidney. Their choice is a testimony to how much more absurd they find materialism.
Nearly all people assume that conscisousness exists, epiphenomenalists are not distinguished in this respect. The general belief in consciousness results from the fact, that everybody experiences himself as beeing conscious.
Epiphenomenalists do not claim that consciousness is an agent in human actions. Because they - like all other scientists until today - cannot show a causal relation between the subjective experience of consciousness and our objective and observable actions. Epiphenomenalists accept the present state of a causally closed physical domain. They do not speculate beyond the limits of present explanations.