@tom_l Thanks! 
I’ll give it a try 
But just now I found this in the logs:
The unit of sensor.rain_lastsixhours cannot be converted to the unit of previously compiled statistics (None). Generation of long term statistics will be suppressed unless the unit changes back to None or a compatible unit.
Go to Developer Tools → Statistics and click the FIX ISSUE buttons.
OK!!
May this be the reason for it?
It’s the only thing I can see wrong with your config.
I guess we’ll have to wait for it to rain, unless you can go and spray the hose on the tipping bucket now?
In fact, I’m not at home right now, but maybe I’ll go over on Tuesday and pour something in from the watering can…
The only problem is that I’ll then mess up everything else: the lawnmower will stop mowing and the irrigation system won’t be switched on for a while although it’s about 30 degrees Celsius for some weeks now staying dry because it “rained” … 
Go to Developer Tools → States
Find and click on your binary sensor.
You can change its state at the top of the page.
Set it to ‘on’ then ‘off’, one tip should register. Hopefully that won’t mess up your automations too much.
Let´s go: just give me some time to set up and test
