Re: toilet that keeps on running
By any chance did you get a Kohler Wellworth?
Two tanks that I got from there were a bit off, where the opening was not round, causing water to bypass the flapper through the side of the assembly because the gasket wasn't centered on the hole. It caused a slow drip, and the tank level dropped down and caused the valve to periodically kick on to refill.
You can confirm this by flushing the toilet, and lift up on the flapper, and shine a flashlight (naturally!) down into the opening, and watch it carefully to see if you notice any dripping. If there is, and you know it's not coming from the center, then that's your problem.
The seal comes preassembled with the tank, so you need a spanner to remove the retaining ring, if it turns out to be the problem.
After the second one, I ended up adding another gasket to take up the gap, rather than return it for a third replacement. Made in Mexico, I think- may have had a bad run (or runs) or something.
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Obvious, but make sure your water level is set properly, and not set too high, where it can trickle over into the overflow tube of the flush valve..