"Think about what a white man would do"
This does contain the essence of your advice; namely, to take credit for work more often, and or more clearly.
My approach is very different.
And I have had the pleasure of mentoring women into male dominated roles a time or two. Fortunately, we were able to establish trust and another male coworker involved in mentoring worked in a similar way. There were challenges, but we made them team ones, not just hers. That made a big difference, IMHO.
What we did was take gender out of it early on, unless it made sense.
In this case, the advice would be, "you should take credit more." And the follow on would be ways to do that and to support the person who will benefit from doing it. That can be as simple as some recognition and sharing later:
"I saw you go for it. Nice! So, how do you feel about it? What happened? Will you do it again?" Etc...
Where gender does come up, that discussion almost always involved a telling of things. And the reason, explained if need be, is just simple understanding.
"How is it for you?"
And that helps with, "what if it were me?"
And then advice makes sense, because there is context, a shared basis.
That is not always needed. Hard to say when it is. But when it is, having it really helps get past or through whatever the challenge is.
I have been fortunate to have women in my life who will share, who I have worked with, who I have helped, and who have helped me. And the things they share have highlighted the fact that their experience is different. Same goes for many attributes, race, beauty, etc...
Often, the barrier to sharing and understanding boils down to some shame, or blame, or admission of weakness, or the perception of making excuses. And while those things can be part of the discussion, it is unhealthy to presume they are, and my experience shows me that presumption happens more than it should.
And that all contributes to how hard this matter is, or can be.
I am a guy, and have found myself discriminated against for seriously considering, "what if it were me?" Or for asking, "How is it for her, or them?"
It is almost like a betrayal, or threat... something I am expressing poorly. Sorry for that, I just do not have precise words.
Often we are asking people different from us to see things from a more familiar point of view. More familiar to us, but what good is that when it simply is foreign to them?
I resolved it this way: we should be seeking a better perception of what it is like for people very different from us. Mutual understanding and respect, consideration.
In my view, there should be no shame in any of that. But there is! And all this is harder.
Since that time, I have paid a lot more attention to these dynamics. Barriers to understanding one another better present real costs and risks that can be avoided, again in my view.