"Mine was doing that at well. It was the water in the tank filling up too much and running into the overflow drain. I was able to adjust the bulb-float and it hasn't done it since."
That should make the water run constantly, not switch on and off, unless your float is balanced just so that it doesn't quite cut off the supply when the water tops off. Since this is a new problem with a decade-old toilet, I'd suspect a leak instead of a bad adjustment.
Thank you all for your suggestions. I'll look into it when I get home.
UPDATE (in case anyone was interested
): I went home and pulled up on the bulb-float and it seemed to work for a while. Then the toilet began to run a little again, on and off. It seemed fine for a day or two and then would run. I never got around to fussing with it further until a couple weeks ago. I don't generally sleep well on Sunday nights and the toilet that is in our master bath - so not far from my head. I heard it go through the cycle twice while trying to go to sleep. Fed up, I lifted the lid and pulled up on the bulb-float again. But apparently I used too much strength as it broke off in my hand! Now the toilet was running with busto and a purpose as it figured the toilet had been flushed. I held up the little bit that was remaining of the bulb arm to stop it but I couldn't let it go to find a better situation (old 70s sitcoms came into my mind at that point). It was a little after midnight so, no, I didn't think about turning off the water at the base. Finally I was able to shove the broken bulb arm under the remaining piece and wedged it in so it wouldn't run. I was still awake (that little incident sort of woke me up even more
) when my husband got up around 1am to use the bathroom. I told him to use the powder room as I had "broken the toilet".
But, happy ending, I called the local plumber at 7:30am that morning and it was fixed a little after 8:00 am (I love small towns). The problem was, as Virg and someone else mentioned, a leak. The rubber seal at the bottom of the tank had warped a little, which they are apt to do after a long time.