A ‘secret rule’ is what I call a trope or archetype that a specific writer comes back to again and again. It might or might not be something that’s universal to the genre the writer is working in, it might be a specific theme or belief that the writer deals with.
For instance, a good example of a trope might be a conservative writer who ever and always has a whiny “liberal” to beat up and abuse. (Mickey Zucker Reichert and David Weber are examples of this. For instance, the prince in The Legend of Nightfall, and various liberal enemies of Honor Harrington are good examples of this.) It might be evidence of a strongly held opinion about gender differences. (For instance, L.E. Modesitt Jr., Marion Zimmer Bradley and Octavia Butler all tend to revisit themes involving the differences between men and women. Most of L.E. Modesitt’s books visit this theme, and the same is the case with both Butler and Bradley in varying degrees.) The archetype or trope is always present in some manner, and in the case of the negative symbol or archetype, the archetype is “punished” for having a wrong-headed world view.
Another way a writer’s personal archetype or trope might appear is in the very fabric of the universe the writer creates. What is absolutely possible and believable in one “universe” is not possible in another universe by another writer. For instance, passive resistance and pacifism does not and cannot work in a story written by a conservative who believes that passive resistance is a waste of time and that pacifists are essentially cowards who let other people do the fighting for them. In the hands of a writer who does not “get” the mindset of military organizations and who sincerely believes that any war is evil–will tend to write military characters as inherently incapable of understanding or wanting a peaceful resolution to a problem. (To test this, apply a basic theme or situation from one book or series to another; if you lift the theme directly and dump it into the situation in the second canon and you abruptly go ‘yeah, no that’s not going to work at all,’ you will probably see what I mean.)
If you know a writer’s symbols and tropes, it is occasionally possible to also get a feeling for the writer’s world view. It should be noted however that it is possible to misinterpret the actual intent of the writer, or misinterpret the trope or symbol the writer uses. A symbol or image makes sense and “works” in the writer’s head may not look the way the writer intended it to, because the symbol has been interpreted differently by the reader.
A “secret rule” is a recognizable symbol, theme or trope that is an intrinsic part of the story, and one that is visited again and again. It might be a specific kind of character, a world view the writer supports or disagrees with, or part of the basic fabric of the universe created by the writer. Spotting and identifying these individualized symbols can give you a sort of window into the worldview of the writer.