The very term itself "wage gap" pretty much highlights the problems with putting too much stock in the wage gap.
The term itself implies an absolute difference in wages, which shouldn't be what anybody cares about.
You should care about the portion of the difference that is due to unjustified prejudice.
Answering that requires a few things that deflate all the interesting pizazz from splashy headlines:
1) You have to specifically define only a single point in the employment process that your statistic will apply to. I.e., you have to say "I want to know the effect of discrimination AT HIRING" or "I want to know the effect of discrimination AT PROMOTION" or what have you. The answer will be different for different points, and you can't meaningfully collapse across them. This makes a single summary number impossible pretty much, and thus a single splashy billboard sound byte that's accurate impossible.
2) You have to painstakingly pick out identically matching cases across every variable possible, except gender. In some cases, this will simply not be possible, or won't have enough data points. Like the issue mentioned above about women's combat gear - you can't really find matching data points with women and men who have identical bodies and need identical gear to compare, because the sex's bodies are different... Maybe you can find a handful, but not enough to analyze.
3) You then need to set up some sort of experimental condition where the decision to be made is parallel between the two sides of each pair, except for their gender, and measure outcomes in a controlled fashion. Looking at past, naturalistic data won't do if you want really accurate results, because you can't guarantee the circumstances were otherwise controlled.
4) You need to now make sure that any differences in outcomes were UNJUSTIFIED, which is not necessarily all the time. Otherwise equally paired candidates applying to be dancers at a strip club and getting unequal outcomes cannot really be said to be an unjustified prejudice (presumably the employer really does need one gender or the other, depending on the business model and patrons of the club).
After all that, you get a number that represents the gap due to unjustified discrimination only, for one particular stage in the employment process. Not very sexy to word it that way, but that's the proper method.
I've only ever seen all this done a couple of times, and it's always been with made-up people (experiments showing a person hypothetical job applications, for instance). The results have been that there is a gap, something like 15-20% if I recall correctly. For hiring salaries, that is. Sadly I can't find actual citations / don't remember the titles or authors.
But if people have studies that qualify with the above, then those are ideal, is all I'm saying.