This is a good example!
In the case of sadness, there are a whole host of associated behaviors that we can observe: people tend to be withdrawn, they might cry, their voice might waver, they're less likely to take risks, their heart rate increases if crying or if not it decreases but breathing increases, and so on. You can even use these measures to hypothetically identify physiologically different kinds of sadness (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5334320/).
When it comes to any individual sad person, we are inclined to trust them when they say they're sad, because people are normally forthright when they admit to sadness. But in cases where there may be ulterior motives (e.g. Depp/Heard trial), we stop paying so much attention to words and actions that can be faked, and try to observe sadness-associated behaviors and physiology because we've convinced ourselves that sadness is a thing by observing people who (apparently forthrightly) say that they're sad, and that thing entails (with some degree of randomness) a variety of changes that we can observe.
So, sadness passes the test: it is not merely an empty phrase to say that "I feel sad"--we do feel sad and we report it to each other, but it is not just the report that we can rely on to know when it's happening.
In contrast, it's much less clear that there is any meaningful distinction between "I identify as a Green Bay Packers fan" and "I feel like I am a Green Bay Packers fan". It seems like it really just comes down to the linguistic choice of the speaker: of course identifying as something feels like something because everything feels like something.
So I guess what I'm querying is what exactly your definition is supposed to accomplish. It's like a strict medical diagnosis of gender dysphoria, except without necessity for distress: "yeah, I feel more like I should be on the other half of the bimodal distribution". But on the other hand it's still transmed-like: "if you prefer some aspects of your as-birth body and the others don't matter to you, you're not trans, even if you identify completely with all the cultural aspects". What if you're not sure about your feelings? Can't you plead the 5th amendment, and just make your choice one way or the other and have that be as good as anyone else's choice? (Counterargument: if someone claims to be a woman/man exactly and only when it would be of greatest benefit to them, are we allowed to doubt them? But would subconscious sex help resolve this?)
If there's actually no operational difference between subconscious sex and "identfying as a woman", why bother drawing the distinction? (I mean, I do have some ideas as to why maybe one should bother. But I'm more interested in your ideas.)