First, as I am sure you can appreciate, periocular hair loss can be triggered by a range of diseases. That said, if we are seeing normal skin, no ocular or ear issues (where discharges from the eyes can affect local hair growth and itching ears can lead to hair loss on the face), itching, and he is on a proper diet; then this does rule out a fair number of concerns. Just to note, with the normal skin, bacterial dermatitis, fungal infections, some immune conditions, and sarcopitc mange would be less likely here. Furthermore, if he is on a proper diet, then trace mineral (ie zinc) issues would also not be suspect here. Instead, we would have to consider potential allergies (though both eyes would like be affected), demodectic mange (caused by a mite known as demodex), and while rare we'd also have to consider Alopecia areata (an immune condition targeting the hair follicles).
In this situation, we can take a few different approaches. First, the most straightforward way to pinpoint which is present, then you could have your vet examine this, scrape this area to check for demodex mites +/- biopsy if they were concerned about immune conditions.
Otherwise, since his signs are mild, you can consider a trial on treatment to see if this settle his signs. To rule out allergies, you can consider a trial on antihistamines. Commonly we will use Piriton (Chlorphenamine) at a dose of 4mg every 12 hours. If you find him very drowsy on this, you can use a half dose. Of course, if he is on any other medication or has a pre-existing health issue then do check with his vet before use.
Furthermore, if we are concerned about possible mild onset Demodex, you can consider treating him with Advocate. This is available at his vets (you may need to pop him in for a weight if they do not have a recent one to ensure the right dose is dispensed) and can be used to clear mild Demodex flare ups. When we use this, we tend to do so, every 2 weeks and you could do so to see if his signs settle before consider more invasive testing.
Overall, these would be our concerns for hair loss of this nature. So, in a situation like this, we could take the above approaches to pinpoint which is causing his signs and get this settled for him as quickly as possible.
I hope this information is helpful.
If you need any additional information, do not hesitate to ask!
All the best,