> Which specific biological mechanism are you hypothesizing is responsible?
Testosterone, causing male-female behavioral divergence in general. Excerpting from an email...
"The amount of eye-contact shown by infants at 12 months of age is inversely correlated with prenatal testosterone (Lutchmaya, Baron-Cohen & Raggett, submitted), and prenatal testosterone is higher in males than females." That study seems to be here: [1]. "The amount of eye contact varied quadratically with foetal testosterone level when data from both sexes was examined together, and when the data for the boys was examined alone."
(Why not for when the girls were examined alone? "This may be because there were only 30 girls in the sample, making the resulting model under-powered. A sample size of approximately 60 would be required to give the model a power of 0.8, assuming a similar effect size...")
There's another one about testosterone in girls [2]: "Here, we report that fetal testosterone measured from amniotic fluid relates positively to male-typical scores on a standardized questionnaire measure of sex-typical play in both boys and girls."
That study also references others that directly show cause-and-effect on other mammals: "For instance, in rodents and nonhuman primates, treating developing females with testosterone or other androgens increases male-typical play, whereas reducing androgens in developing males reduces it."
To me, the question isn't whether testosterone affects behavior, it's how much.
[1] http://docs.autismresearchcentre.com/papers/2002_Lutch_eyeco...
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2778233/