Gas countertop KitchenAid stove ignitors continue to spark even when all knobs are on off position. I unplugged the stove so as not to kill ignitor altogether.

If you are saying the clicking continues you must move the burner knob past the LITE position.
If it continues clicking with the knob past the LITE position the ignitor switch behind the knob is bad.

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It sounds like the ignition knob is stuck in the "ignitor" position. Try taking it off, clean it and adjust it. If that doesn't work, it will have to be replaced with a new one. If yu leave it alone, it will probably wear itself out. Just make sure that the gas valves on the stove are in the off position so that they don't accidentally light on their own. Good luck

Just solved this on the Kenmore model 911.33389 (same unit). Ignitors started with no one touching the cooktop. It has had a history of doing this and, this time, sparks were visible under the knob. Disassembled cooktop (don't forget to unplug and shut off the gas!). Performed "smell test" for burned electronics. Found smell in #3 ignitor switch. Disassembled and found worn, burned, and fried. Parts list was inside unit but had a typo for the "ignitor switch". Showed WB18T10240. Ordered that only to discover it was the transformer to ignitor wire harness set (no photo on website!). Wrong part... ugh! Dug deeper for the correct part #. It was WB18T10239 but it has been replaced with WB18T10344. Noted on some website that someone installed one and then the ignitor was NOT synchronized. Turns out, you can install WB18T10344 about three different ways. Mine was 22 degrees off vertical (different than original) and now my unit works perfectly! Also, install the new switch harness (if that's what you do) starting from the left front valve then clockwise. The original unit installed from the right front valve, then clockwise. Hope this helps.

THAT IS THE IGNITOR FOR THE GAS. TURN THE KNOB JUST BEYOND THE START POSITION AND IT SHOULD STOP. IF NOT UNPLUG THE STOVE AND FIND THE IGNITOR ON THE BURNER HEAD AND CLEAN IT WITH A SOFT TOOTHBRUSH. PLUG THE STOVE IN AND IT SHOULD STOP CLICKING

We just had that problem - the igniter is electric - if none of the burners are "clicking" it could be a power problem. unplug the stove and check whether the outlet is working. In our case, the outlet the stove is plugged into has a "GFI outlet with a reset button. So we reset the outlet and that fixed the problem.

it is strange that you have no gas and no spark! if you held a match to the burner and turned the burner valve on it would lite di spite a failed ignitor,but for it not to lite, the burner valve[its what the knob attaches too] would have to be blocked[thats rare]or ........i got it .....the knob is broken.thats the only thing the burner valve and the spark ignitor have in common.try a knob from another burner................again.you have spark,because others are working.spark on troubled burner would work if valve blocked at orifice outlet,and if spark failed you would still get gas they work independent of each other,[but in unison].thats why im thinking knob.its the item that works both .when you turn the knob it opens the gas valve and as the gas valve rotates by turning the knob it activates or turns the spark switch so it closes the curcit allowing the electricty to the spark moduel.hey i hope that helps a little. God bless ,tom

On any range I've seen with electronic ignitors, the valves have a position that closes a contact to turn on the ignitor and manually moving the dial to the 'Hi' setting opens the contact again and the ignitor ceases to spark.
You don't mean the ignitors run even when the burners are off, do you?
I'm surprised to read that this has been happening for 'years,' the transformer for the ignitors must be really tough to withstand that and it doesn't sound like an electrode or transformer problem but rather a contact not opening as it should or you not advancing the control past the ignite point.     

Turn the knob back towards off about 1/8 of a turn and you will take it off lite and it should fix it.

some JA models i have seen the the spark switces are poorly constructed or improper installed from the factory and beging to become a probelm after a year or so of use. this is not a gas pressure issue it just plain ole' bad spark switches

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