What are some techniques used to structure symbolism in a movie? Watching Kubrick's films makes me wonder if there is more than one layer of symbolism, because unlike other movies there are so much depth and so much possible meaning that you can come up with deeper and more meaningful interpretations the more you watch them. Is there any techniques that are widely used to structure and layer in extra layers of symbolism? Or is it like the wild west and there's absolutely no rules or consensus on how to do this and how to interpret a film?
It's a question of an artist making their art. Or in fact, several artists; the director, actor, set designer, costume maker, make-up-artist, etc, and last but not least the scriptwriter. They all add symbols or content and meaning to the film.
They may in turn lean on education, artistic genius, and many other things, like an ongoing cultural exchange of ideas among people active in their business, genre, etc.
Then there's the more scientific or structured approach to symbolism.
This usually comes from some form of studies at a special art school or university from film science (or theater science or literature science) to acting or directing schools.
In most of these educations, the topic of semiotics will be brought up as one of the most used tools for constructing and deconstructing meaning and symbolism of any and all elements in a text, movie, or theater performance. See especially film semiotics. It also exists for literature.
Semiotics considers everything, small and large, a semiotic signal, and that it provides meaning. From a blinking light in the hallway to Death with a Scythe. From the costume of the characters to the weather, and everything else that appears on the silver screen, book page, or theater stage. (And in paintings, comics, etc, if it can have meaning, it has semiotics.)
There's also the intuitive aspect. Intuition is of course an important part of everything from artistic expression to scholarly semiotic interpretation, but there could also be this, "I don't know why" intuition in play. And it could of course stem from anything from artistic talent to society debate to dreams and songs...
Sometimes someone might just say, "we should have a blood-soaked screwdriver here." Even if it doesn't necessarily fit.
There might be a debate among the people in the production about the blood-soaked screwdriver and some will love it and some won't, but the director says "Ok" (or maybe it was their idea from the start) and there's a blood-soaked screwdriver.
Other parts of the production might start commenting on it when they form their own interpretation of the blood-soaked screwdriver, and it might become this thing.
Reviewers might go "why?" or "wow!" (or "boo")
Society at large might start debating blood-soaked screwdrivers (regardless of if the blood-soaked screwdriver was placed there by intuition, semiotics, or because this other movie had a blood-soaked hammer). This discussion could range from "ouch" to the builder's union starting a debate on workplace safety to a deep dive into the real meaning of a blood-soaked screwdriver in such an unlikely place... what does it symbolize? What do they want to say? Why?
And the production has reached one important goal. Make people think... even if it only was about blood-soaked screwdrivers and their connotations. Or make people talk about the movie so other people will buy a ticket to watch it as well... Depending on who you ask...
Of course, then everyone is free to use semiotics (or anything else, for instance just have an opinion) to create their own interpretation.
Especially theater is unique in this aspect. A theater performance is a once-in-a-lifetime experience and if you and the person next to you focus on different things on the stage, your interpretations may vary... With movies and books, you can go back and revisit, with theater that may only be possible to a certain extent. (Obviously, there's a lot of other things influencing interpretation as well...)
Analyzing movies (or anything else that has meaning) is, in the academic context, more about building a reasonable case for a specific interpretation than being right or wrong.
Update: Then, of course, we shouldn't forget all different types of sources of symbolism such as archetypes, both archetypal characters and archetypal stories (the Hero's Journey for instance, or Russian folktales), myths, and other religious texts as well as religious practices around the world, magic, angels, runes, numerology (for instance, the number 47 in Alias), etc. A dictionary of symbols might reveal even more sources. And some sources are arranged in a system. E.g. numerology (1, 1, 2, 3, 5?), or elementals (no fire without water? air without earth?) etc.