This is not medical advice, I am posting this for educational and information purposes.
I could not eat anything without getting ill. I seen many studies showing toxins absorb through the skin. Since I could not get my nutrients from food especially cholesterol, our body needs a lot of it. So I started using oils and some of them I would infuse with things that had nutrients. For example cucumber is high in choline so to get my choline I infused an oil using cucumber skin. My health improved dramatically. So I do believe transdermal vitamin patches work though the research on them is scarce.
Transdermal vitamins are not very effective unless they add something to cause the skin to absorb them. But the research shows using alcohol on the skin before applying the patch causes more of the nutrient to be absorbed.
When we have sulfation issues we can absorb magnesium sulphate (epsom salt) through our skin. Even when we have high sulfide levels it will not make a person ill because it is a type of sulfur the body can readily use. If you get sunlight afterwards it will help reduce certain hormone in the body that the sulfation issues have cause.
Vitamin E protects the skin.
Vitamin A can absorb through the skin but can irritate it.
Our skin does contain enzymes to break down nutrients.
Many studies have shown that essential oils are absorbed through the skin.