Air Tahiti Nui has those deals quite often - definitely sign up for their newsletter.

The thing that surprised me the most the first time I went to Tahiti was that the flight really isn’t that long, only a bit over 8 hours from LAX to Papeete. I don’t know why but before going I had always felt like the flight would be more of a looong adventure like it is getting to other places in the South Pacific (like the full day + of flights and sitting in airports that it takes to get to the eastern part of Indonesia).