In the early years of the band and ShowBiz Pizza, he was positioned on Beach Bear's surfboard. This was done for a specific reason, early versions of the Frog had eyes that were attached to springs. When Beach Bear would rock back and forth on his surfboard, the Frog's eyes would pop out and bounce around.
Later on, the eyes changed color and became blue (they were red previously) and the Frog was moved to the Center Stage floor and became a decoration.
During Concept Unification, which took place at nearly all of the ShowBiz Pizza locations between 1990 and 1992, the Frog (along with most of the other props on the center and left stages) was removed completely. After these events, the prop was likely either destroyed, put into storage, or sold off to a collector.