The bullseye dial has been a popular watch design for over many years. Many watch brands have their own model lines based on this bullseye. In the Forties, Fifties and Sixties Timex and Kelton had several bullseye watches in their product range. They weren't called bullseye though. The 1971 Sprite Bullseye was the first to be named as such. 

Sprite - 23170 - model 24 - 1973

TIMEX Electric Bullseye

Another bullseye model was introduced as Electric in 1970 and came in calendar and day-date configuration. These models all had a bezel, either a diver bezel or a worldtimer bezel. In stead of the red, white and black colours of the Sprite Bullseye, the Electric Bullseye has a light blue ring on a dark blue dial.