“Other signs of possible Vitamin D deficiency are oily skin or acne.”
I don’t know what you mean by that.
This can be explained by the role of Vitamin D in cellular metabolism. Vitamin D is essential to the process by which the mitochondria in cells convert triglycerides into adenosine triphosphate (ATP), the body's molecular fuel.
Inadequate vitamin D in its active form thus tends to cause elevated triglycerides because they are not properly metabolized by the cellular mitochondria. The elevated triglycerides then lead to oily skin.
This can be especially evident on the nose and face. Vitamin D supplementation with increased sun exposure can help alleviate oil skin.
In addition, inadequate Vitamin D impairs immunity. This can permit otherwise common bacteria to take hold in oil clogged pores in the skin and cause acne.
In short, if you want to clear up oily skin and acne, part of the remedy is to take Vitamin D3 supplements and get more sun.