It might be worth pointing out that "gender" originally meant "the observable but non-tangible aspects of sex" when it was coined in the 50's. The "social roles" definition is the newer aspect.

You can observe someone's gender in the same way that you can observe any other emotion; you can feel happy or sad, and while some people are better than others at hiding it, you can tell when someone else is happy or sad (and understand their feelings through the lens of your own). We all make the decision to get out of bed in the morning (or not), we know everyone else does, and so we can be aware that the will to do something other than sleep all day exists.