If I recall correctly the supply ship goes a round trip between Pitcairn and Mangareva which means you can get off on Pitcairn and wait for it to come back from

If I recall correctly the supply ship goes a round trip between Pitcairn and Mangareva which means you can get off on Pitcairn and wait for it to come back from Mangareva. I went on a chartered yacht being operated by a Pitcairn based tourist venture. Choices then were to stay for 2 days or 11 days. I stayed for a month due to the charter yacht needing to leave and then return with a department of conservation employee to investigate a rat sighting on Henderson island. There were many private yachts visiting the island while I was there, coming and staying for a few days then leaving.