I have not seen the original picture you show but there is another on the internet with Jim Reeves, Bobby Bare, Anita Kerr, and Chet Atkins all sitting together. Seems like it was taken at the same time. Chet Atkins is hold a piece of paper or small card. All are amused. I can only assume that somebody has added a mobile phone and erased the card.
It is very unlikely that icons like those were in use in 1964.