The click you hear is that holding coil that blocks the flow of gas when the gas assembly fires off. The sensor and ignitor or wired in series with each other with the coils. The coils themselves will not work because the ignitor hogs most all the current, when the bimetal inside the sensor gets hot enough then it opens and kills the power to the ignitor. The coils get a rush of shocktricity and open. The gas flows out onto the blazing hot ignitor and Whoosh!!!ya has fire. That holding coil tends to get hot and quit with a little age. I don't think the coils are it I would say the sensor or the ignitor is bad. One way to check, is to grab the wires off the sensor and YOU be the sensor. With the dryer running hold the 2 wires together till the ignitor is glowing brightly and then seperate the wires. The gas should come out. Have somebody handy to unplug the dryer.