I finally got to checking my 1957 service manual, and this range does not show up. The less deluxe 40" models (J403 Stewardess, J405 Speedster, and J406 Mainliner) look like the picture that Sandy posted, though the Stewardess does not have the clock. The deluxe 40" models have the controls above the glass panel, like the stove that is for sale, but all have the larger lighted burner control switches ('tel-a-cook'). These stoves are the Stratoliner (deluxe single oven range) and Liberator (deluxe double oven range). So I think Mark's guess sounds logical... the less deluxe models moved to the new design backsplash/control panel, but continued to not have the larger lighted switches.
Sandy, to your point in another thread, all of the standard 40" ranges have the divided burners (two burners on each side, with large area in the center) and the deluxe models have the 'cluster top' with the burners clustered on the left side.