It is fairly common for an indicator light to stay on even when all the burners are turned off. On some designs each switch has its own indicator; that's an easy one, replace the bad switch.
However, many cooktops have a single indicator for all the burners. If this light stays on, finding the offending switch is the tricky part. The best method is to open the back of the console and remove the P terminal from one burner switch at a time. Insulated pliers can make quick work of this diagnosis. When you remove the indicator wire from the bad switch the light will go out. Now you know which one is bad!
"Hot Light" Stays On
Glass tops add a second independent indicator, the element is "still hot" indicator. This function is controlled by a pencil shaped sensor that crosses the top of each ceramic burner. As long as the sensor is warm the hot light stays on. Repair usually requires disassembling the whole glass top and replacing the entire element.
