I have two Sterling 1.6 gpf toilets in my three year old house that have the same problem. I have a trickle of water coming from my tank into the bowl which lasts for five to ten minutes then it stops. You notice this when looking directly at the bowl at 12 o'clock.
I do not have any water dripping from my fill valve and I've tried different flappers. I just replaced the flush valve with a fluidmaster flush valve kit as that has a new flapper and seat. This did not resolve my problem.
Has anyone else had this problem before I resort to calling a plumber?