I have one of those low, squat, Koeler toilets that were popular in the early 90's (one-piece). I had the innards completely redone about 3 yrs ago. Worked fine until a couple of months back when it began periodically running. At first, it was once in awhile---now it's every flush. I replaced the flapper, but it didn't solve the problem. To make it stop I have to turn on a faucet in the house briefly. Occasionally, when the toilet is quiet and I turn on a faucet, it will run (not flush, just run) then stop 5 secs later. It also will stop if I raise the arm with the big black ball on it just for a sec. Any ideas? It's driving me crazy. I feel like the cobbler whose kids have no shoes, as my husband used to be a plumber before Alzheimers came calling.