I have a GE 30 inch electric cook top. 2 days ago the biggest burner, it went out, it tripped my electric fuse switch. Now when I turn the fuse switch on, the indicator on the biggest burner shows its hot even when the burner is off. I have no idea what the problem is. Please help.

Are you sure it is fused, don't think so.

Faulty switch if you are changing it yourself remember turn off power and take your time, take a photo to compare so you get it right.
Good luck. Ray

you have melted internal wiring, probably some mice ate it. call an electrician and DO NOT USE IT!! turn off at the wall/fusebox

I've seen this problem before. It happens when spillage get's into the ignitor switches. The switches are mounted on top of the gas turn-on valves. You have to replace all the ignitor switches because they are connected into wire harness. Rich

You may have a short circuit to ground fault in the electric cook top. Divide and conquer. Unplug the cook top and try to reset the breaker. If the breaker resets, then you have a problem with the electric cook top. If it doesn’t, then the problem is at the electrical panel side. Either problem will require a qualified technician’s assistance. I hope this helps. Good luck.

As it relates to 5 burner gas cooktop Model Number JGP 963SEJ1SS
First - Ignite the flame then reduce the flame to between low and medium.  If the igniter continues to click, you most likely have a contact switch issue related to the problem burner.  
Unplug the cook top and turn off the gas.  After the gas is turned off, disconnect the gas line.  
Remove the cook top.  

Unscrew and Remove ALL of the burner bases by lifting them up.  The ceramic igniters may be difficult to remove but they will come loose if worked out slowly.  
Pull of the wire connected to the igniter. 
Remove to cook top top plate from the base, exposing the internal gas valves and wiring.
All of the burners are wired in parallel.   Lift off and unsnap the casing of the problem igniter switch.  The repair may require something as simple as, 1- cleaning the contact strips, or 2- slightly bending the non stationary contact strip to keep it from coming in contact with the stationary contact when in the off position, or 3- replacing the switch. 
Unless you comfortable and understand how electric systems and switches work, this is a job for a qualified repair person. 

It's the Switch Harness. Do not remove the stove and disconnect it from the gas. Turn the gas off under the stove. Take off the: knobs and the plate; burners; hxw screws. Pull burners out and disconnect igniter burners. Lift the top of the oven off. The Switch Harness is on the right, under where the knobs are located. Replace the Switch Harnes.

Don't really need a wiring diagram, although there may be one inside switch area. (make sure to put it back again if it is there) Will need the full model number to get you the part number you need. (model number usually on a sticker near where the electrical wire enters the cook top)
Turn off power to cook top. Open cover to switches. Pull two "pilot" (usually smaller spade terminals) off the switch for the right front burner, and insulate each with a bit of electrical tape. Turn power back on to see if light now off. If yes, replace that switch. If no, replace those wires and repeat procedure with the next switch until you find the bad switch. Send a comment if you need additional help.

Confirm there is 240 VAC powering the unit (make sure a breaker has not tripped or a fuse blown.).

Did the burners ever produce enough heat?

If yes, then we can look deeper. If no, then the burners may not be adequate for your cooking style. Burners are like light bulbs. A 60 watt bulb will put out more light than a 40 watt bulb. A 100 watt bulb will put out more light than a 60.
Typically, a small burner will provide less cooking heat than a large burner.

How old is this cook top stove? Does it require replacement?