As reported in The Twilight Zone Companion, Rod Serling initially thought he had invented the phrase “twilight zone,” but later learned it was an aviation term. His older brother Robert was an aviation writer; perhaps Serling heard him use the phrase.
The phrase was certainly “in the air” at the time. Raymond Chandler planned to write a novel titled Zone of Twilight; he never wrote it, and died before Serling’s television show premiered.