I often see women closing their eyes and concentrating after lighting Shabbos or Yom Tov candles. I was told that this is an auspicious time to pray. I would like to know if any commentators discuss exactly what a woman should or shouldn't pray for at that time and if there are any text which should be recited.
The following is from Aish:
After the recitation, many take special time to thank God for the many blessings of health, prosperity, and joy in their lives. There is also a special prayer composed by women, for women, which many include at this time:
May it be Your will, Lord my God and God of my fathers, to be gracious to me (and to my spouse, children, parents) and to all my family; grant us and all Israel good and long life; remember us for good and blessing; consider us for salvation and compassion; bless us with great blessings; make our household complete, crowning our home with the feeling of Your Divine Presence dwelling among us.
Make me worthy to raise learned children and grandchildren, who are wise and understanding, who love and fear God, people of truth, holy and attached to God, who will dazzle the world with Torah and goodness and service of God. Please hear our prayers, in the merit of our matriarchs Sarah, Rebecca, Rachel and Leah, and ensure that the glow of our lives will never be dimmed. Show us the glow of Your face and we will be saved. Amen.
It is a time to talk to God. So express anything that you wish, and ask for all that you desire. He wants to hear your prayers.
During candle lighting she should be thinking about fulfilling the Mitzva of honouring the Shabbat by creating a brighter room.
After she has extinguished the match, covered her eyes, made the Bracha and then looked at the candles and accepted Shabbat, she may want to use this auspicious time to pray for whatever she feels needs to be prayed for.
The Kitzur Shulchan Aruch in 75:2 mentions that it's a good time to pray for help with educating children.
וְאִשָּׁה קְשַׁת רוּחַ בְּגִדּוּל בָּנִים אוֹ שֶׁאֵין לָהּ כְּלָל, סְגֻלָּה שֶׁתֹּאמַר לְאַחַר הַדְלָקַת הַנֵּרוֹת, הַהַפְטָרָה שֶׁל יוֹם רִאשׁוֹן דְּרֹאשׁ הַשָּׁנָה. וְטוֹב שֶׁתָּבִין מַה שֶּׁהִיא אוֹמֶרֶת, וְתֹאמַר בְּכַוָּנָה.
After doing any Mitzva one has created an auspicious time, as far example after Birkat haMazon one prays for multiple things, in the various HaRachaman requests.
I think that you are confusing two things. While my wife does say something after saying the bracha (I will get that and add it to the answer), closing the eyes is not part of concentrating or saying something other than the bracha.
There is another reason for a woman to close her eyes at the lighting of the candles for Shabbos. Technically, she should first say the bracha and then light the candles. However, once she has said the bracha, she has accepted Shabbos and is forbidden to light the candles. Thus, she lights the candle, put the match or lighting device away, closes her eyes, says the bracha, and then opens them to accept the "new" light after the bracha.
Note that she does not close her eyes until after she has extinguished the match or other lighting device. She does not close her eyes while lighting the candles.
Again technically, she would be allowed to say the bracha on Yom Tov and then light, since one can light from an existing flame. However, for consistency and so that she could extinguish the match or put away the lighter, most women will act as they do on Shabbos.
I believe that Rav Soloveitchik reported that this was how his mother lit the candles on Yom Tov.