Gender, Gender, Gender, and Gender

I am going to do something unforgivable. I am going to ask the meaning of a word.

What does 'Gender' mean, when used in the context of 'gender identity'?

Before I started paying attention to the gender debate, I thought that what was being said was, more or less, that some people deeply felt that they should have been born the other sex, and that we should treat them as if they were that preferred sex. What's actually being said is that biological sex doesn't really exist and that whether you are male or female depends on your gender identity, not your physical body. So it seems kind of important that we know what this term, gender identity, means.

I've asked this of many people - politicians, people who work in civil rights organisations, people who agitate for the primacy of gender identity over sex. I've only ever got three kinds of answers:

Silence - the most frequent (non) response.
Circular definitions - eg., 'Gender identity is the gender you are', 'gender relates to your gender identity'.
and Negative definitions - 'Gender isn't biological sex, or stereotypes, or personality type'.

I have come across various uses of the word where it means something in particular:

1. It's often used as a synonym for biological sex.
2. People who hold that male and female people have distinct, innate patterns of psychological traits sometimes refer to that as 'gender'.
3. Second-wave feminists believe that 'gender' is the system by which female people are conditioned to be submissive and male people are conditioned to be dominant.

Second-wave feminists, among others, believe that the concept of gender identity actually does refer to the second and third meanings. That the idea of an innate gender identity suggests that men and women really do have distinct patterns of psychological traits, and that these traits are in line with the socially-prescribed roles of men and women. As second-wave feminists believe that those socially-prescribed roles are detrimental to women, they naturally reject the idea that female people are fundamentally suited to those roles.

So second-wave feminists see gender identity as regressive and sexist. Given the understanding of the word 'gender' by second-wave feminists, it's unavoidable that they think this.

Meanwhile, people who promote gender identity see second-wave feminists as regressive and transphobic, because they object to the replacement of sex with gender identity.

I am a second-wave feminist, I think. I certainly don't want to be regressive, which is precisely why I currently have a problem with the concept of gender identity. It appears to me to be regressive. It doesn't matter how much hate I get for this position, I can't go along with something I believe is sexist and harmful to women. What would make me go along with it? It's simple - if I could see that it wasn't regressive, that it was, in fact, progressive.

For this to happen, I'd have to know what people mean when they use the word 'gender' in 'gender identity'.