First, yes! To me 'essence' = homunculus!

Was there ever a time you felt both or neither genders?

[These are MY answers and don't necessarily speak for all trans or non-binary/gender-fluid people]
Prior to beginning to come out in my early 30s, I had kind of given up on the idea of intimacy and focused more on my intellectualism and developing personal philosophy. This was my closest to feeling 'neither' gender since I had accepted the idea of being single, found social gratification with friends (even if not intimate) and defined myself outside of gender lines. I was my soul, passions and ideas...all of which are essentially gender irrelevant in the traditional sense.

I'm not sure how much other feel this way, but I tend to think of myself more since coming out as what has been called 'Two-Spirit.' While I still feel and choose to present female, I do still have and understand a male perspective to a degree. In some countries this is revered due to the insight and knowledge from both sides of things. But much as we travel up and down through Maslow's Hierchy of Needs, my male/female needs and proportions flow as well.

However this is much deeper and I'm trying to understand how that works since gender is such a vital part of identity in general

While I can't deny biological sex, I've wondered how much effect society has in actually defining gender. It's nearly impossible to seperate especially with it being so deeply rooted into out languages. He/she pronouns are use countless times a day, when really a gender neutral term like they/them could easily be used, but why? Why do many languages like french, spanish and italian have a masculine/feminine applied to everything. (It is la bibliotèque not le bibliothèque) What sense does it really make to apply gender to inanimate objects? This is really a hard one to separate since for many people conscious concepts require a word, and those words have un-noticed implications. I get the concept of 'gender role' in the evolutionary biology/psychology sense, but it really doesn't explain why it's still held to tightly or embedded in our vocabulary.

Great question!