I used to do something similar with the I Ching - I sat somewhere between detached skepticism and an elaborate sorta-scientific story about how it might actually work. I think I wanted to believe, and so I made myself "pretend-believe", you might say. Does that sound like your experience? It sounds a little like you enjoy pretending to believe, without really believing in witchcraft. (And just to be clear I have no problem with that, at least until the pretend-beliefs start encroaching into action the way real beliefs would.)
And I still think the I Ching is remarkable for being so suggestive for thinking about puzzles (though I don't use it any more). It takes a certain skill to write 64 different entries that sound meaningful and yet could apply to just about any question. I guess that part's like the placebo effect in your example.
I Ching is wonderful poetry but as divination, it's an experiment and always will be. Because there is skill involved in divination, I constantly keep track of my tarot card predictions and see how close to true they turn. When I do this consistently, the readings get better and more on the mark. Divination is utililizing reading people, emotion and predicting human behavior and dynamics to most probably outcome of a situation. We can do this without divinatory tools, but the tools sometimes help the brain get there. If any card or I Ching role can apply to anything, then the interpretation is not exact enough and pretty useless. There are better diviners and you should experiment with one, see how specific predictions can get and how close to the mark they eventually get.
Pretending to believe I did for the visualization process of my spells for some time. You have to dive in headfirst to give the experiment and legs. But after awhile of doing this and seeing results, seeing what actually produced results and which spells or aspects of spellcraft didn't work, I had faith in certain experiments, like you would have faith that if you dropped something from your hand it would fall on the ground. After awhile, you know the circumstances and how to open your hand to produce the desired result. I usually use the word faith for faith in something else, and knowing for knowing a spell will work, with a critical eye to double check that knowledge of course.
As you probably know, these experiments aren't of much use unless they're double-blinded, because of the incredible power of confirmation bias. As a step, you might write down very specific predictions, and also a bunch of specific things you don't predict as though they were predictions. You might do 30 predictions and switch 15 of them to the opposite prediction, maybe. Keep track of which are which, but use labels only you know (like a triangle and a square, say). Then ask others to help. Ask one person to rate each prediction on its specificity and surprisingness (for example, "you will meet a handsome stranger" is not specific, while "the sun will come up tomorrow" is specific, but does not require tarot to predict). Then have some other person look at all the predictions and fake-predictions you made, and mark which ones came true. Make sure they have no idea what the labels mean, and make sure you are not anywhere nearby giving subconscious cues while they do these tasks. You should just hand them the predictions, labeled in a totally generic way (so not plus versus minus, for example, which has connotations), and let them rate them. This still isn't a well-designed study, I would say, but you get the idea. Tarot's predictive power is only confirmed (some) if you get surprising, specific predictions right significantly more often than your non-predictions get marked as right.
Also: I don't have faith that if I let go of something it will (in typical circumstances) fall to the ground. I have very good truth-related reason to think this will happen, based on what I know about gravity, past such events, and so on.
Then spellcraft is reason, after awhile and repetitive work. The study sounds interesting for someone more concerned with the process and scientific analysis and less for something more interested in its practical applications. When you said leave before you give away subconscious cues, well, most of witchcraft is about harnessing and manipulating that subconscious. Not to say confirmation bias is the only thing going on in a tarot reading, many other things such as a woman unhappy with her relationship is eventually going to leave it just because that's the most probable outcome, basic predictions people who study psychology can do fairly easily, as well as confirmation bias. That's why the job of a tarot reader has to be taken seriously and with a sense of morality. We guide the people we read for using the philosophy of the stories in the cards, which is basically just this philosophy that things are cyclical and any end is a beginning, you know, basic uplifting stuff. Much of tarot reading is also reading the current state of the person, which we get confirmation of in the moment by their subconscious cue admitting what we said was true. And for specificity, we just look at how happy someone comes out of the reading, do they know something more about themselves or the path they choose to follow, or are they left thinking it's a hoax. If the latter, not specific or a good reading. Tarot isn't actually about predictions. It's one part current emotional state, one part meditation on a problem, and a very small spice of most likely outcome to come from the emotion and problem, which psychologists have been able to predict with these double-blind studies and authors because they just study and write about people all the time.