Right rear single element stays on - KitchenAid KESC300 Electric Kitchen Range

Not in my experience but what year is it. Did you install the correct bulb the correct way. Check if you have a double element bulb in a single element socket or a single element bulb in a double element socket and the double element bulb can be installed in the wrong orientation.

Could be both parts are faulty from symptoms you describe.
The indicator light should not be on if it is in the off position, this would suggest the thermostat is faulty.
On the other hand, if the element is faulty, then obviously, there will be no heat
To be certain if the element is faulty or not, then you need to test the element with a meter.

It is without doubt the element that has blown.
It is located at the rear of the oven compartment behind a removeable cover.

Hope this helps solve your problem

he is right in what he says the heating element is feed from the main control board

the trun signal and brake light are on the same bulb or element the running light is in a different bulb single element some cars have three bulbs with one element and they are 1157 1156 and so on.

If the fan is working, but there is no heat from rear element, then the element needs replacing.
Remove inner rear cover of oven, you will see the element there, remove, and replace.
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If the fan is working o/k, then you need replace the oven element.
To access this, remove inner rear cover of oven, there you will see the circular element.
Unscrew the screws securing it ,and remove element.
Detach wires and transfer to new element, be careful not to lose the wires behind the oven rear, refit element and rear cover.

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Remove cover at rear of oven compartment, there you will see the element.
Undo fixing screw(s), carefully pull the element towards you, remove wires, be careful not to lose them inside ,and fit onto new element.
Refit element and rear cover.
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Thanks.

Hi.
If the fan is working o/k, then you need a new fan oven element fitting.
Remove panel at rear of oven compartment, there you will see the element, undo any screws you can see to remove rear cover.
disconnect element taking care not to loose wires, and fit new element. test before you refit rear cover.
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If element stays on even with oven turned off you probably have a bad main board. A relay on board is probably stuck on. If it stays on, but at a reduced heat...not getting red hot, it may be from a shorted wire causing 110 volts to get to element.