Each burner has a sensor on it- you will need to determine which one is stuck by trying to tap on the small box-looking part on the burner that has some wires attached to it as that will typically work. The whole burner would need replacing as the sensor part is not usually available by itself. FYI- nothing is harmed here by that light being on, so judge whether it is worth the expense of repair as this can happen anytime to any other burner too.
ok, I looked again at the tag on the frame
made by sears
model no(NNN) NNN-NNNN/p>
the 8 looks like 8 but could be a B
the stove has spiral burners which fit into a simple plastic connector. hot and neutral wires from each connector lead into the switch panel on the back of the stove.
from what i can see the light that is staying on is not a light that tells you the burner is hot but simply to tell you that a burner is on. the problem is within one of the four switches. the easiest way to find out which one is causing your problem is to unplug the unit then remove the rear cover of the control panel. then follow the wires from the indicator light to the switches. you will see that this wire simply jumps from one switch to the next. remove it from the first switch it goes to then plug the unit back in. if the light is out then that is the switch that needs to be replaced. if it is still on the replace the wire and remove from the next switch and repeat until the light goes out. when the light is out then you know that is the switch that needs to be replaced. what has happened is the contacts have stuck together in the switch for the indicator light. only smooth tops have an indicator to tell you that a burner is hot. the coil burners just tell you that one is on. once you find the bad switch, rf,lf,rr,or lr, i can get you the part number and price.