Two small parts inside the tank are almost always responsible. One is the flapper, a rubber disc that seats over the drain and is meant to hold water in the tank between flushes. The other is the fill mechanism that senses the water level and stops the refill once the tank is full. When the flapper sits crooked or has gone stiff with age, it lets water slip past continuously, so the fill mechanism keeps working to replace what’s escaping, and that constant back-and-forth is the sound you can’t get to stop.
Neither part costs much, and either one is a quick swap once identified. What’s worth asking, though, is why it failed early in the first place: Davie’s water carries enough dissolved mineral content that rubber components here tend to give out sooner than the same parts would somewhere with softer water.