Semaphore, I'm remembering exactly the same one. I think it was a fence -- kind of like a sand break -- that the plane ran into when it landed on the beach. And Dean Martin was one of the deceased pilot's friends, and to figure out what had gone wrong, eventually took an identical plane up to re-create the flight.
I guess some of the people on board had survived, because I remember a stewardess (as she was called then) telling Martin, who was flying, that at that same point in the flight she'd entered the cockpit and given the captain coffee. So Martin told her she should give him some, because he didn't want to miss any detail, no matter how small. Then he put the coffee on the center panel, and eventually it fell over, and he got the same "indication" as the first pilot would have. And I think Martin then turns off an engine.
But it's already been established that one of the engines had developed a problem. So the false indication had led him to turn off the wrong engine. Martin re-starts the one he stopped, and all is fine.
He has some line at the end about how his friend's death wasn't in vain, because now the consoles would be sealed differently -- or maybe the pilots would be told not to put their coffee cups on them -- so lots of lives actually will have been saved thru his friend's death.