Halacha forbids preparing on the first day of Yom Tob for the second day. For example, if Rosh Hashanah falls on Thursday and Friday (as it does this year, 5775), it is forbidden to make preparations on Thursday for Thursday night or for Friday.
In light of this prohibition, it would appear, at first glance, that women must wait until dark before lighting the Yom Tob candles on the second night of Yom Tob. On the first night of Yom Tob, of course, women generally light candles several minutes before sundown just as they do on Ereb Shabbat. On the second night of Yom Tob, however, if they light candles before dark, when it is still the first day, they will be preparing on the first day for the second day. Seemingly, then, they must wait until dark before lighting the Yom Tob candles on the second night.
This issue was raised by Tosafot (Medieval French and German Talmudists) in Masechet Besa (22), who observed the practice in their communities not to wait until dark before lighting candles on the second night. Tosafot claim that this practice is acceptable, because the candles are being lit shortly before dark, which suffices to avoid the prohibition against preparing on the first day of Yom Tob for the second day. Moreover, when one lights candles toward the end of the day, he derives benefit from the light immediately, as there already is not all that much light. And even if the room is already illuminated, nevertheless, the candles add more light, such that one benefits from the light. Hence, the candles serve a purpose even for the first day of Yom Tob, and the lighting is thus permissible.
The Bet Yosef (commentary to the Tur by Maran Rav Yosef Karo, author of the Shulhan Aruch) cites Tosafot’s ruling, and then proceeds to note that Rabbenu Yeruham (1290-1350) brings a view that disagrees with this position, and requires waiting until dark before lighting on the second night of Yom Tob. In conclusion, however, it appears that the Bet Yosef accepts Tosafot’s lenient ruling, and this is the position taken by several later authorities, including the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work Rab Pe’alim (vol. 4, Orah haim 23). Additionally, the Shela Ha’kadosh (Rav Yeshaya Horowitz, 1558-1630) notes that if a woman waits until dark before lighting candles, she will be sitting in darkness all this time, which would not be an appropriate way to spend Yom Tob, and this is another reason to permit lighting before dark.
This is the ruling of Hacham Ovadia Yosef, in his Hazon Ovadia – Rosh Hashanah (p. 182; listen to audio recording for precise citation). Therefore, on the second night of Yom Tob, women may light candles at the same time they light on Friday afternoon or on the first night of Yom Tob.
Summary: Although it is forbidden to make preparations for the second day of Yom Tob on the first day, women do not have to wait until dark before lighting candles on the second night of Yom Tob.