About Eris, the rulership I believe is a higher octave of Gemini, the nature of the planet is like Thoth - an embodiment of the universal mind - communicating a message for the world is what this planet is all about.
When I was studying the planet, I called it Persephone-Xena, but later, I felt Thoth made more sense, Eris is a nice name, but it is naive to take the symoblism much further without analyzing it in the charts of people:
the name Thoth makes a nice parallel to Eris but i think a vital thing it ignores is the femininity of the planet . Why can't there be a female planet which encompasses these universal communications? (the original greek messenger god was the female Iris) Women have been so short changed when it came to the naming of the planets- Luna (moods) and Venus (boyfriend troubles) don't exactly accentuate the native intelligence of women, and face it, women wrote the book on Trickster...(not to mention most of the best astrology books!)
"embodiment of the universal mind"- yes! it seems Eris may have a way of bringing out the universal unchanging forms, like an elephant suddenly materializing in one's living room! i'm inclined to look at Eris (with Mars) as a higher octave of the Sun