Second time around I noticed the "how long has it been around?" subtext. The easy answer is a few decades, that goth came out of punk (or was punk internalized). Certainly many of the early goth bands (Siousxe & the Banshees, Alien Sex Fiend, etc) centered around the Bat Cave in London, as well as the ones in LA (Rozz Williams Christian Death) were moving out of punk and into what later came to be known as goth. It is not verified but commonly accepted that Siousxe herself coined the term. Goth, more or less as we know it today, started back in the late 70s. And yes, there are 50-year-old goths. They're really jaded.
The etymology of the term is as follows. Rome was sacked by Visigoths, or Goths. No, they weren't into fishnets, absinthe, liquid eyeliner and bad poetry. But they were connected (I forget how, perhaps geographically?) to the gothic arch, which was the heart of gothic architecture. A lot of people thought gothic architecture was pretty spooky, and some people started, in the Victorian era, to write spooky novels about spooky things which often took place in spooky settings like gothic cathedrals. Thus the terms "gothic novel" and "gothic literature" were coined to describe these stories. And a "goth" has become someone who reads too many of said stories.
Goth has also been connected with Romanticism; it has, in fact, often been refered to as "new romanticism". I kinda hate to admit this; I thought "The Sorrows of Young Werther" was awful. But the main tenets of Romanticism find pretty direct paralells in goth. But the ideas of man alone in the face of nature/the universe and empathy/intuition above reason find pretty direct correlation.