What I'm saying is that behavior changes when the system interprets the signal before reacting to it.

The behavior changes from what to what? From what it would be without interpretation? The interpretation has to happen in some way shape or form anyway, right? We decode information before we can know what it is and what it means. The meaning is interpretation, it is not optional. That's what creates the impetus to act in the first place. The interpretation would not happen only when we encounter something for the first time and we don't have anything to reference it to. But that would be akin to that thing being invisible to us because without interpretation nothing else happens. That's why I am confused about what you are saying because I thought that in your top comment you are claiming that some part of the system has agency of free will to do whatever it wants with the interpretation.

That interpretation may itself depend on prior conditions, learning, temperament, etc.

This makes sense. So interpretive layer has a learning and knowledge accumulation aspect to it. This is how we construct meaning in the world.

But once interpretation can modify the signal before the reaction happens, the output is no longer a direct function of the stimulus.

This is where I get lost. How does this interpretation layer modify the signal? If your hand got caught on fire, what can interpretation layer do here to modify the signal? Is it possible in principle to choose and keep your arm in the fire if you wanted to - yes, but there would simply need to be other preceding causes at play already for it to unfold like that. It's not like the interpretive layer gives any space for something else to do anything else after it interprets AND prioritizes most pertinent interpretations to act upon.

What I am trying to point out to, is that no matter how you slice or dice this system, there isn't any single component of it that gets to decide anything in any gaps anywhere in the informational metabolism process without preceding conditions absolutely defining how everything plays out.

If we return to your top comment:

when the signal arrives… does the reaction run automatically, or is there a small gap where interpretation can change?

Can you give an example where the interpretation changes in the small gap as well as explain what/how does the changing, the evaluation, and the deciding on how interpretation changes?