The minimum wage was pretty stable as a percentage of the median wage in New Zealand until recently. Nonetheless, the gender wage gap narrowed at the bottom of the labour market rapidly in the 1980s and 1990s.
In common with the USA, that narrowing of the gender wage gap stopped in the early 2000s after the minimum wage started increasing as a percentage of the median wage.
Again, that is contrary to the idea that the minimum wage is a failsafe that narrows the gender wage gap at the bottom. This failsafe is said to be the leading reason why the gender wage gap is much smaller at the bottom of the labour market than higher-up such as the median and in particular at the top.