I think that I would define gender as part of your innate sense of self. This definition differs from sex, in that sex tends to be understood to refer to physical characteristics. That being said, I am perfectly comfortable saying that my sex is female, despite the fact that I am pre-op. I am also on hormones, and my external body is in all other ways characteristically female.
As far as gender characteristics are concerned, we are all an amalgamation of gender characteristics, and there are very broad continuums - even among cis people - between stereotypically male and female personality traits, and even physical traits. I think that one definitely does not decide the other. Plenty of straight cis people have traits which overlap in this way, and it certainly doesn't define them in any way as being trans or gay, or anything in between. It is that innate sense of self, of your core identity, which tells you whether you are trans or not. And there are many people - many of whom identify as gender queer - who feel that they are both, or neither, and this is equally valid. This is where you begin to fall into distinctions between what is socially constructed about gender, and what is innate. This such as whether, for example, I like action movies or romantic comedies (I like both), whether I played with "boy" toys or "girl" toys as a child (again, I played with both), and whether I dress femme, or more butch or androgynously (I'm pretty femme), are essentially cultural ideas of male and female, and, again, there are plenty of cis, strait people, for example, who overlap across these lines, and one does not define the other. As far as what is innate, I maintain that I am innately female, because that has always been my internal sense of who I am. It is visceral, and part of my core. The trans community itself presents an extraordinarily broad continuum that includes intersexed individuals who do not identify as either male or female, all the way up through transexuals who do aim to entirely change the gender and sex into which they were born. There are no right or wrong answers to the question of what your own transition or trans identity means to you. Wherever you fall within this continuum, I promise you that there are others out there who are like you, and who feel the same way that you do.
As to your specific question about permanent cross dressers...I've never heard of it specifically, but I wouldn't be surprised to hear that there is at least one person out there who identifies that way, and I refer back up to what I said above. My understanding is that many people who identify as cross dressers identify their gender being consistent with the sex they were assigned at birth. I am also not very well-versed on the subject of cross dressers and ->-bleeped-<-s, I fall into the transsexual, entirely changing the gender and sex into which I was born side of the spectrum, and I just have not spent as much time investigating these other aspects.
I hope this helps : )
