I fully agree with what you're saying. In philosophy it's often described as something physical, and so it stands to reason that it would leave physical evidence. It's difficult to observe the brain while it's still working, but that doesn't make the mind fundamentally inaccessible.

The biggest problem, though, is that it's just not very well defined. In some contexts it's been defined by reaction, as you mentioned, though that definition has to be refined for more complicated applications (e.g. in anesthesiology where awareness might remain when reactions are suppressed.) Phenomenal experience and qualia are terms usually used to narrow the topic down to the mind-body problem, but even they have multiple definitions, and some of these definitions can lead to the conclusion that qualia don't even exist.