Earlier quoted context omitted.
We obviously will never agree since functionalism and my form of somewhat-physicalism are at complete odds. But I do want to understand your position more. You say that the physical hardware your enigma simulation runs on provides the causal element. But the simulation of the nuclear reactor also runs on physical hardware. Yet it obviously doesn't provide the causal element, and neither does the enigma machine simula…
Let's start in the middle, where you say I wrote "When you have digitally modeled a brain such that the model responds to its inputs as a brain does, then you have built a brain." What I actually wrote was this: "Then, presumably, you will also hold that when you have digitally modeled a brain such that the model responds to its inputs as a brain does, then you have built a brain." This has to be read in the context…
The reason I brought up the enigma machine's hardware is to illustrate there is a difference between the physical machine and the abstract program that it can be observed to implement. However the machine can be used for more than that, for example I could use it as a footrest, or I could dissemble it's parts and use it to build a bomb. I could simulate this as well, but nothing would actually get blown up.
Physical implementation alone does not show that every property of the simulated system has been instantiated. Reactor software is physical without fissioning nuclei, a simulated enigma can't be turned into a real bomb. What reason do we have to think consciousness is fixed entirely by functional/causal organisation, rather than depending on substrate-specific physical properties of brains? This is the gap I talked about, although rather clumsily I might add.
And reproducing the formal or input-output structure of a process does not automatically reproduce every intrinsic causal property of the thing simulated. If consciousness is intrinsic (and I think it is, my pain does not become pain only because an outside observer interprets my neurons as representing pain), then by contrast, a bit pattern in computer memory means “pain” because of how a program and its users interpret or employ it. It's problematic to explain an intrinsic phenomenon entirely in terms of observer-relative symbol manipulation rather than as a physical property, which the simulated brain would lack.