I don’t agree with Gillespie’s ‘99% certain’ estimate but he makes a very strong case for Earhart and Noonan having searched along a ‘line of position’ (navigation term) to find their destination Howland Island, perhaps not going far enough north but there is no land that way beyond Howland, instead turning south toward the Phoenix Islands.
The estimate is that they crash-landed on a reef, were able to transmit at low tide for a few days, but a storm destroyed their airplane.
Credible DF on radio signals pointed to Gardner Island. (Notably those by experienced Pan American stations. Pan Am flew the Pacific to the north of that area. Radio signals were at frequencies giving long range at certain times.)
(Gardner Island is now called Nikumaroro.)