GE Cooktop Model JP340B0J2bb

You need the switch for that burner. The contacts inside are stuck together. You will need to pull the unit and separate the glass from the lower body to access it. To get the right switch you need full model and serial number located on a plate at the bottom of the unit.

Your ability to perform this is dependent on how mechanical you are. The Whole unit must be removed from the counter opening and the base unscrewed from the glass, remove knobs before disassembling. For someone mechanical this is not difficult. De-energize whole unit first.

Once the two pieces are separated the remainder is mechanically easier. Disassemble the box on right containing the switches and replace the correct one. Reverse the process for reassembly. Good Luck

Source: Burner only cooks on high heat.

I'm having the same problem with my jec9530. The dual burner just quit working one day. I called jennair and they sent me a replacement "custom control" for free. 6 months later it quit again. I am now considering attempting to put an infinite switch (dual), part #PS786568 in its place. It is not electronic, and it looks like it is used for the jec9536 middle back dual burner. It is only $35, even if it doesn't work like the electronic one I don't care. My wife usually only uses both burners at the same time anyway.

Source: Inop burner on new jenn-air JEC9530 elec flat cooktop

the very first thing i would do here is to check the ignitor itself
under the head cap you should see two screws, once those are out you will be able to lift the burner plate, lift the burner plate, you will see, or should see the ignitor, and the wire.
i check this for voltage by unplugging the ignitor and olding the wire close to a ground, the metal body is good. Turn on the ignitor, becareful it is live. yhou shgould see a spark comming from the wire
if not check to make sure that wire is in position and on the spark module
if you do see a spark this way, just order the replacement ignitor
and install it when it arrives
appliancepartspros.com
part number AP3191250

Source: The igniter on the right front burner of my GE Gas Cooktop

The outer ring of the element is most likely broken. You'll need to replace the element.

Source: electric cooktop burner malfunction

There are a series of holes in the burner leading down from the main flame area to the pilot tube, ensure the holes are not plugged/restricted.

Source: Kenmore Elite 30" gas cooktop installed. Large right front burner