90% certain it's a leaky "flapper" - I left the water turned off for a couple of days while we were out of town and the water level leaked right down to the seal of the flapper.
Here's the problem. It's brand new. I just bought & replaced the thing. But that didn't fix it. So I bought brand new seals. And that still didn't fix it. But I don't have fluid leaking out of anywhere else, just this flapper.
Aside from constantly turning the water off (or sealing the thing with concrete, which I really feel like doing after several months of fighting this thing), is there a way that I can get this thing to stop ghost flushing?