That's a nice thought, but the real promotions often happen on the grounds of "leadership", "management" and "communication skills", which women are often perceived to lack.
Or maybe you work in a more egalitarian place than me.
If anything, I think women generally have _better_ communication skills than men.
You do realize that we're talking in vast generalizations here. Engineers run the gamut; there will be sexist, racist and bigoted engineers too. But my experience in nearly 20 years of being in the field has been that engineers, _in general_, are more egalitarian. If someone comes up with cool shit, no one cares whether that person is a woman, or a man, or what color his/her skin is; if it's cool, everyone goes "oooh!" and s/he gets instant respect.
What's eye contact for, anyway? I can read body language reasonably well, but I always feel like people are expecting me to do something with my eyes and I can never tell what, exactly, I'm supposed to do with them.
Basically you're supposed to look at their eyes for 5-7 seconds at a go. Then look away but not at their chest (regardless of sex). Flick to something behind and above them, glance at a window or clock or other feature in the area.
If you don't like their eyes, focus on the bridge of their nose, they won't be able to tell the difference.
For neurotypicals, it creates sensations of companionship and trust, until it goes on too long and then it becomes creepy and uncomfortable for them.
Some of us have significant hearing loss. Eye contact (better stated face contact) provides a lot of non-verbal cues as to what the %!*^&%! you're saying. It's not quite lip-reading, but I think it's getting additional information about where the syllable breaks are.
Or maybe you work in a more egalitarian place than me.