“The appeal of the birther issue was, ‘I’m going to take this guy on, and I’m going to beat him,’” said Sam Nunberg, who was one of Mr. Trump’s advisers during that period but was fired from his current campaign. “It was a great niche and wedge issue.”…

But for all of his fascination with the president’s birth certificate, Mr. Trump apparently never dispatched investigators or made much of an effort to find the documents.

Dr. Alvin Onaka, the Hawaii state registrar who handled queries about Mr. Obama, said recently through a spokeswoman that he had no evidence or recollection of Mr. Trump or any of his representatives ever requesting the records from the Hawaii State Department of Health.