I have a few anecdotal experiences that support the gender/pay theory, but I know of only a few studies and the matter is extremely complex.
I come from a legal family and from what I see in Australian law gender matters, as the individual lawyers "gravitas" influences judges decisions, standing and likelyhood of advancement (concrete and "sociopolitical"/ingroup/boys club). Female lawyers have less gravitas, plain and simple. The profession is skewed to wealth, age and conservatism, and the even the left wing tends to paternal and Fabian rather than radical. Female lawyers who are granted positions of authority or rank (eg SC/QC or magistracies) are marked out for private mockery and excluded from subtle but significant clubs, rankings etc. There's stiull traces of "Old School ties" religious and University bias, University of Melbourne has lapsed its standards badly but is still by reputation the premier legal educator because [conservative chortling].
Can't find the two studies ATM but when i was studying feminism (I had to take some non-history units and chose something out of my field) in the 1990's there were some comparative studies on similar industries to see if there was a gender/pay gap. Librarians (70% female) were compared to geologists (90+% male) who had similar levels of education, budgets and assets under their control etc) on the theory they were comparatively specialised groups numerous enough to make reasonable comparisons (there's a ****load of geologists in this country, we are basically a large mine). The other one was nurses to some other field, I forget which, not doctors, something with a similar spread of education/qualigfication requirements and repsonibilities.
IIRC the pay gaps were significant even when adjusted for "lifestyle" eg having children. Having children interrupts seniority progression which is a fairly wildly accepted concept in this country, but alternative systems like ongoing training/relevant experience are also interrupted by having children. The nurses pay gap was influenced by the vocational ethic in the industry which meant they have only ever gone on strike properly once ever. Typically Australian wage negotiations can be influenced by walk outs etc, even in fairly educated fields like Geology (if you strike it shows you'e serious, but also sometimes Union Officials and bosses work out the wages lost during a strike period will cover a bonus payment so a deal is done to get a zero cost win for the Union), but the nurses only ever imposed the mildest of work bans because of some Florence Nightingale myth and the hospital administrators had used them like peasants because of this.
Is this a voluntary wage cut accepted by women? Is it wage structures favouring coded "male" behaviour financially (not getting pregnant and not giving a rats about walking out the door to strike)? The arguments around both the cases did lead to some improvements (but the nurses had the go on strike, just the once, and the fallout led to bitter acrimony in the union) and ultimately the arbitration system in Victoria accepted the argument about librarians too IIRC, so our system recognises that women have been penalised for their gender and makes redress.