Furthermore, take note of how Adam tries to put the blame on Eve rather than taking responsibility.
I did take note of it. I also took note of the fact that Adam didn't grab a piece of fruit on his own, he took what Eve gave him.
Eve may not have said a word, but the act of giving someone something carries an implicit assurance that "it's OK". Adam's job as head, at that point, was to tell her "NO". He didn't do that. And that's (again) the context of the passage in 1 Timothy: deciding who has the authority to teach.
IMO.
YMMV
IANTP