Many, many years ago I use to work for NOAA. We had these rain gauges that work as follows.
There was a small rectangular metal container balanced on a pivot. It was maybe 4 to 5cm long. Kinda like a little metal bucket. In normal situation the rain bucket sat level, but as it would rain, the bucket would fill and pivot. The pivot action would trigger a microswitch. You could use this concept to have the trigger drive a relay. Then again, if morning dew is not an issue, I would say boncuks idea is the way to go
One more thing. We sometimes had problems with bird poop triggering the gauge...lol