Well, I think the 1/3 rule comes as a roundoff of the Golden Mean Section (0.618) in classic painting, which is slightly closer to the center than 0.667 (2/3) -- artists are math challenged, if you give them a 0.618 rule, they can't remember, you know that.
The Golden Mean Section on a blank canvas (or Tabula Rasa, if you prefer a classic term for a classic concept) draws our attention the MOST in the frame, so painters tend to put the point of interest at a GMS spot -- horizontally or vertically.
Bulls eye works when you have a near symmetrical situation, NOT when you have asymmetrical objects at the 1/3 rule spots vying for attention.
Edges and corners are also attention grabbing places. Yet most of the time, we use it the wrong way, leaving a tree limb near the frame, for instance, therefore distracting. If you see MIKE's photos, the edges and sides are clean.
Eyes placed at the corner or near the edge can be very strong, but that's more of a modern approach.