Most toilets in Germany have two buttons. One for flushing and a second one for stopping. Some have one button and stop flushing when you press that second time, but those tend to work more unreliable. Another variant: One button that's a kind of a toggle switch that you flip to one direction to flush. It toggles back once it's done, but you can flip back sooner to stop flushing.

Seems there's a market over here for water-saving toilets. The toilet vendors are creative.

By the way... I have never seen the variant you are describing, but hey...