I find the nodes extremely important, but I wouldn't look at them as sign rulers because of their "general" nature. They have their basic meanings but are completely colored by their position in a sign and a house.
Idem for Chiron. I find Chiron important, because it can tell you a whole lot about natives' subconscious tendencies, thus influencing the interpretation of the whole chart.
A Leo/Aries, with Moon conjuction Chrion in the 12th house is completely different from someone who's Chiron placement is, say, in the 11th not aspecting his Moon.
I like Chiron in Virgo, for their obvious similarities. For the nodes, I take NN for Aries, SN for Pisces. My idea is if NN and SN are mix of energies, then perhaps in my postulation NN is more Sun -Fire - Aries. SN is more Moon - Water -Pisces. I am reading that both nodal points can be quite powerful NN with self-ambition, SN selflessness.
... There's an ancient view that the NN, the "Dragon's Head", is Exalted in Gemini, most highly exalted at 3 degrees.
Exaltation and rulership are different, I was answering to a question about rulership
I have read an interesting article on the exaltation in Gemini (NN) and Sagittarius (SN), I can't remember where, in the context of the antisica of the solstice points of the Cancer/Capricorn axis, which correspond to the Gemini-Sagittarius. Which could be one explanation for the exaltation of the NN and SN in these signs.
Symbolically it makes completely sense. Still, by practice and his mythological character I see Chiron as Capricornian.Well, the fact that the Sagittarian Centaur IS literally Chiron in the Ancient-Greek mythology is what causes me to have it ruling Sagittarius.
I have the SN as a co-ruler of Taurus. That aside, what's your description of its affect on the chart? Maybe something about empathic and/or psychic ability?