this is entirely unrelated, well sorta related and I'm going to make an analogy to my trans status later however, first we start with this sense. I have given this sense quite a bit of thought, mainly because I do not possess a full sense of proprioception whilst completely blind. If I am aimlessly wandering in a barren room, I will literally stumble and fall unless I'm against a wall or another object. In my case a cane works well enough for this sense to come to me, however, I can only sense it if I'm using force and an object is there to enact newton's third law.
This is an interesting thing, because I often find, before I had a solid understanding of my gender, I felt like I was walking in an empty room, that goes on for miles with no cane or walls. Without my prosthetics, I feel real weird, unstable, as if i'm going to fall over. I lose my ability to act confidently in a real world situation, I essentially lose my ability to be myself. Gender identity, in my experience, is absolutely the same as proprioception, it's the same innate feeling. So, in the end, I'm basically just adding to your post, I guess. However, I think it's useful, maybe.