Gilligan's Island S02E12 - Don't Bug the Mosquitoes

The members of a popular rock band known as the Mosquitoes (played by The Wellingtons, who do the Gilligan's Island theme for seasons 2-3) come to the island to get away from their fans so they can practice their music in peace. When the castaways find out that it will be quite a while before they can get off the island, they try to get the group to leave early.