Hmmm...I always started counting with December 25 = 1st Day so that January 5 = 12th Day; eve of Epiphany therefore Twelfth Night.
You may very well be right. I had thought that 12th Night celebrations happened on the day of Epiphany itself -- the last fling of the feasting before ordinary time again started the next day.
In the West, Epiphany is linked to Christmas thematically, since it commemorates the coming of the Wise Men, so it made sense to me that Epiphany itself would be the 12th day. I may be completely wrong in my memories.
In Orthodoxy, Theophany (Jan 6) is not thematically linked to Christmas in the same way. Since we commemorate the Baptism of Christ, at which the "worship of the Trinity was made manifest," it is not linked to the events surrounding the birth of Christ the way it is in the West.
We actually read the account of the Wise Men at Liturgy on Christmas Day itself, as the culmination of the Christmas story. The Old Testament prophecies of Christ and the other Gospel passages regarding the birth of Christ have already been read by that point (at the Royal Hours in on the morning on the Eve, at the Vesperal Liturgy around mid-day of the Eve, at at Matins of the Vigil of the Nativity.
There is even a delineation between Nativity and Theophany by making the Eve of Theophany a strict fasting day, just as the eve of the Nativity is a strict fasting day. Liturgically, Theophany is actually a higher ranking feast than the Feast of the Nativity in the Orthodox Church.
There is more liturgical hoopla for us at Theophany as well, since that is when we do the Great Blessing of the Waters (both in the Church for the year's supply of holy water at at the nearest large body of water), and when the priest goes around to all the houses of parishioners to bless their homes for the year.
More than you wanted to know. If you find out definitive answers, let me know.