Electric gas igniters sometimes get stuck in one position causing a clicking sound. The clicking sound that you hear is the electric arc that is pulsing from the igniter conductor (wire) to ground (the gas burner). It receives power from the electrical outlet that the stove is plugged into.
Residue from food and sometimes cleaning products may be preventing the igniter from producing a spark (Arc) to the base of the burner. This is a common problem that occurs when the stove has been cleaned or food is allowed to build up. Make sure that the igniter and the burner base are clean and dry. This will help with proper operation. Oven cleaner and a small tooth brush may be used to accomplish this. Another problem with ignition may occur if you have too little (touching) or too much space between the igniter and the base of the burner; it will prevent the burner from igniting. You should only have a little more space than the thickness of a nickel between the burner base and the igniter. A good “blue” arc from the igniter to the burner base is optimal. If this doesn’t work, you may need to replace the electric igniter module. Good luck.