Cliradex was created by world-renowned Ophthalmologist and researcher Dr. Scheffer Tseng. It was tested specifically for the eyelid, lashes and face. We do not have specific studies for the scalp, but the properties of 4-terpineol can apply to any skin type, including the scalp. It is extracted from tea tree oil, and its properties are the same regardless of the skin. So you could use Cliradex on your scalp.
The foam is just as efficient. It is a lesser concentration for everyday use. This is the study on the safety and efficacy of the foam - https://bmjophth.bmj.com/content/3/1/e000094.
Conclusion: "The above finding suggests that 2% T4O formulation is safe and effective in killing microorganisms related to common ocular and skin infective diseases.”