I can actually buy the explanation of sailors believing that it improved eyesight. One of the things that I have studied extensively as an herbalist and in particular my specialty, Ayurveda. which comes from India. I have been studying ts connection to the Middle East and points onward is that the piercing of ears, noses, etc. all have a tie-in to bodily health. In acupuncture, and its predecessor, Ayurvedic medicine, depending upon which point is pierced, helps stimulate a bodily response that does enhance health.
Also, unrelated but yet related sort of, women in India (and elsewhere) pierce their left nostril - it is tied into creativity / creation and fertility, as well as enhancing her femininity. ;-)
Acupuncture works, so hey, if it worked, I am sure a pirate might be an easy adapter of similar customs during the era.