When Jeannie is under the pool table and rolls to face away from the camera, she nods her head (as when blinking), but there is no sound effect.
Jim Backus, of course, played millionaire Thurston Howell III on the castaway comedy "Gilligan's Island". However, he isn't the only former regular from that series to appear on the show. Series star Bob Denver (Gilligan himself) appeared in the third season episode "My Son, the Genie" as Hadji's son Harold.
Jim Backus must have been a huge pool fan. During the first season of "Gilligan's Island" one episode featured a scene that included a game of pool. Also, Backus appeared on an episode of "The Brady Bunch" during that show's final season as Mike's boss entitled "The Hustler", which also was centered around the game of pool.