you have a good idea. but I'm not convinced its a REALLY accurate test? reason I said this is we need more chemical info. For example: if we mix red dye with a bowl of sugar, all the Sugar turns red. But if we mix red dye with bleach, yes the bleach turns red, but the poisonous chlorine gas that will emit if one were to next add ammonia to this brew will not be red. So...I'm concluding your dye idea is a possibly good test, but may or may not be accurate to answer our question!
I am wondering if there is some chemical reaction happening between the olive oil and the emsom salts along with bile and other liver chemicals, one that maybe goes way beyond simple staining with colors of components. I'm thinking of some chemical reaction that causes solids to precipitate out of the liquid.
I have an experiment I thought up. I have chickens. Some of the older laying hens eventually get butchered for broth making. One of them could be given a blk walnut tincture worming, then later, after she is no longer passing parasites in her manure, give her a liver cleanse using the same ingredients as we would take, but in smaller quantities based on her size/weight versus us people. Keep her in quarantine so we can watch what happens. The reason I think this may be a good way to know is that in years and years and years of butchering various farm animals I've never seen one single stone of any size or color or kind in livers or gall bladders of farm animals.
Of course I'm not questioning that SOME people do have such stones, I'm wanting more evidence that the high, high quantity of stones being passed by people doing the Liver Cleanses are ones that were really there all along and not new ones chemically precipitated out by the injested ingredients. I'm guessing that if my chicken passes zero stones, and then later she is butchered and her liver also can be examined along with her gall duct...and if no stones are evident...then that seems pretty convincing to me that the cleansing ingredients have nothing to do with it. But if she does pass stones, I'm going to personally think it is caused by the cleansing ingredients. Again, because she'll be a first ever chicken in my own experience to have such things.
The problem now is timing and when I'll be able to do this experiment. Cold season is about upon us and I wouldn't make a faithful hen stay alone in an outside cage until nice Spring/summer weather arrives.