Now based on your history and photos, it does appear that we have a non-itchy non-skin altering hair loss here. This would make infectious issues like mites or fungus less likely (which is why the other donkey is without signs). As well, the lack of skin changes make issues like bacterial infection or other parasites less likely as well.
With those most common issues aside, we would need to consider hormonal issues (less likely with only one side affected), autoimmune hair based issues (ie telogen and anagen effluvium, etc) seasonal alopecias, nutritional deficiencies or chemical exposure (again less likely with jus tone affected), and diseases that result in defective hair shafts (eg, trichorrhexis nodosa, etc). As well, we can see loss of coat quality and unpredictable hair loss associated with underlying systemic diseases (so if he has an underlying organ or metabolic issue).
Now with these to consider, I do have to note that you will be limited with what you can do at home. In cases of this nature, we tend to need to analyse the hair follicles +/- take a skin biopsy to pinpoint which issue is present. Furthermore, since we can see this secondary to internal issues, checking a basic blood panel and overall check-up would also be ideal here. That said, since you noted that the hair is quite dry, it can help to support him with essential fatty acids (EFAs). Specifically, you can supplement with flax or fish oil supplements intended for horses to help with coat health and promote regrowth while we further narrow the root cause for this in your lad.
All the best,