The gender wage gap by part-time status is small because men and women find themselves in very different part-time jobs. There's more heterogeneity within part-time jobs for women compared with men. Men are more likely to be in retail sales part-time jobs, whereas women can take on a variety of different part-time tasks. The labour force survey has information on self-employment, but I think it only has annual earnings associated with that, and not an hourly wage rate.
On May 2nd, 2016. See this statement in context.