OK, it is new to me. I frequently read this forum and have not seen it mentioned.
Starting last year a new train service, Campania Express, was stared between Naples and Sorrento. It runs 4 times a day only from mid March to mid October and only has stops at Naples, Herculaneum, Pompeii and Sorrento. It is called a tourist train. You can make reservations and be guaranteed a seat..