A gas stove burner that makes a clicking sound when the gas burner is turned on might be caused by moisture or dirt interfering with the surface burner ignitor, also known as an ignitor electrode or a spark ignitor.
The surface burner ignitor electrode is located on the burner and emits a spark that ignites the gas on the burner creating a flame. Overflowing pots, grease and other cooking debris can interfere with the spark. Try cleaning the surface burner ignitor electrode and the area surrounding it with a tooth brush, or a nylon scrubbing pad to remove any dirt or grease covering these parts. Allow the parts to dry completely before assembling and testing the gas stove burners again.
A persistent clicking sound could also indicate an issue with the ignitor switch or spark module.
The ignitor switch is mounted on the surface burner valve stem and supplies voltage to the spark module. It is controlled by the knobs on the stove. If the ignitor switch is faulty, it might be a reason why the gas range surface burner might not light.
Another part that could be causing a clicking noise on a gas stove is the spark module. The spark module sends an electronic pulse to the surface ignitor that helps light the gas on the burners. After checking the surface burner ignitor switches, check this part to see if it needs to be replaced.
Keep your gas range stovetop clean and make sure the burner portholes are free of grease and debris to allow the proper gas flow to ignite the burner.