It was an early form of electronic communication where Morse Code was used to send messages by wire.

John Emmet O'Brien has written:

'Telegraphing in battle' -- subject(s): Accessible book, History, Military telegraph, Personal narratives, United States Civil War, 1861-1865

That was Mr. Samuel Morse himself, who proved that it could be done by submerging a cable in the NY harbour and telegraphing through it in 1842.

In 1851, the first commercial submarine cable was laid on the bottom of the English Channel by the Anglo-French Telegraph Company, connecting France and the UK.

This may refer to when a person is giving facial cues or other signs that they are nervous and they "telegraph" their emotions. It can also apply to any emotion that is revealed by watching the person's body language. While job interviews can make a person uneasy, the best thing to do is just be yourself and answer the questions honestly, to the best of your ability.

Reaction... if trained properly.

Reaction is instinct and so it happens without conscious thought. This means many milliseconds are saved. (Think of how if you accidently touch something hot your body reacts and pulls your hand away without even thinking.)

Action requires conscious thought, and many people end up telegraphing what they will do next with their eyes or other body movement.