taṇhā specify gender, then kamma make it.

You need to recite paṭiccasamuppāda-pāli & ariyasacca-pāli. Everything perfectly and completely taught in tipitaka.
Rebirth (jāti, upattibhava) depend on avijjā & taṇhā (upādāna) & kamma (3 saṅkhāra, kammabhava).
3 taṇhā = kāmataṇhā, bhavataṇhā, vibhavataṇhā (sacca-pabba).
Whatever is good kāma/bhava/vibhava (piyarupaṃ, sātarūpaṃ) such as beautiful nun, is what is attached by kāmataṇhā/bhavataṇhā/vibhavataṇhā such as you love to sense about nun/you love to be a nun/you love to leave your male faculties (purisindriya).
Bhavataṇhā cause of kamma, so the example cases are:

1. Your love (kāmataṇhā) to sense (kammabhava) about nun, will cause a male rebirth.
2. Your love (bhavataṇhā) to be (upattibhava) a nun, will cause a female rebirth.
3. you love (vibhavataṇhā) to leave (upattibhava that cause of the other difference kind of upattibhava) your male faculties, will cause a female rebirth, that is difference kind of male rebirth.

You can receive bad effects in every gender, so tipitaka and commentary never specify the gender as an effects of kamma, except when the gender is a very significant cause of good/bad effects, such as purisindriya/itthindriya. For the example, a woman must release blood every month, so a regular woman often week more than a regular man, in physical body. So in regular case, female rebirth is suffering more than male rebirth.
However, that example doesn't mean that tipitaka of commentary specify the gender as an effects of kamma. That example is just an effect of kamma-bhava that depend on taṇhā. So, if male in the example has an enough strong taṇhā, he will not rebirth as a woman, but he can rebirth as a bloody man instead.