The was a huge scandal there recently due to some men initiating the young girls. When the men returned to island, after conviction at trial, including the islands leader, no one on the island cared a hoot about the crimes or scandal. The island did not like their dirty laundry being aired to the world. Since then it has become a little more insular.
There is a another South Atlantic Island, or should I say group of Islands, that has very little in the way of covers, and that would be the South Sandwich Islands. During the Falkland War, and WWII some of the islands were occupied and I believe on and off there has been a research station on the islands, currently in use. Unbelievably, even though it has no native population it has a deputy postmaster, probably not the busiest job in the world. Now if you really want to get into rare South Atlantic covers, look to the island of Thule. You will see Thule Island stamps in a lot of Scandinavian collections, they may exist on covers, although they are, I believe, Cinderellas. Norway had a presence on the island in the last couple of years of WWII, hence the Norwegian Cinderella’s (kind of like Lundy). However the Argentinian naval station that was there just prior to the Falkland War did send mail from here, although it was franked in Puerto Santa Cruz and cannot be differentiated from the local mail from there, unless on official cover. Lastly the whaling stations of the early 1900's on these island, did produce some mail, I have had in my possession, as a dealer, some Falkland Island stamps franked South Georgia, they are scarce. For more on this read this article..
http://www.philatelicdatabase.com/p...encies-1936/