Are brown spots on the skin, more commonly known as age spots, strictly caused by photoaging from sun exposure over time, or are they perhaps viral in origin?

This is another brilliant insight you had about the possible consequences of viruses in the skin being associated with the problem of age spots. This is a combination of influences from both presence of virus as well as exposure to sunlight causing a protective effort of the skin that is aggravating the viral presence and its consequences, resulting in excessive melanin production.