The rain sensor that you show isn't a very good one. It can detect normal tap water fairly well, but not rain water.
It works by detecting an electrical short between the two sides of the sensor. Tap water and most river/lake water (not rain) is electrically conductive. When a drop of water hits that sensor then it will conduct electricity across it. The reason why there is that "dual interlocking comb" pattern on the PCB is to increase the chances that a single drop will touch both sides.
The reason why it will not detect rain is this: pure water is NOT electrically conductive! The water must have dissolved minerals in it to become conductive. It is possible to submerge entire PCB's into pure water and have them function just fine (until the water is contaminated). Rain is basically pure water. There are some things in it from dust and pollution, but it is pure enough to cause sensors like the one you show to be unreliable at detecting rain.
Most commercial automobile related rain sensors use some sort of IR system. I will let you google that one yourself. You can easily find all sorts of diagrams, drawings, and even aftermarket sensor kits for your car.