From the look of the flowers, it seem that when the petals are bent backwards, they are ready for pollination. I read somewhere that this happens for tomato flowers. Eggplants and tomatoes belong to the same family. I have noticed that the eggplant produces two types of flowers. One with a centre thingy which I believe is the female part (stigma). The yellow parts are the male parts or anthers where the pollen are stored. I remove one anther at a time and peel it gently (it is very delicate) to reveal the white pollen which flies off fast in the breeze. I would dap this onto the female part. Hope that this works to produce eggplant since I read that bees are not attracted to eggplant flowers :
The other flower is similar except that the centre part is either non-existent or very deep inside and tiny. This flower cant seem to be pollinated and I am not sure what it is for :