It could be one of these seals leaking.
I have 5 Briggs Vacuity toilets in my house and they are all about 7 years old. Two of the 5 periodically "run" unattended--the water level in the tank slowly drops to the point that the float drops and the tank refills to the top level.
I have replaced the flapper with a genuine Briggs repacement (I too have discoved that other brands do not work well) and cleaned up the seats--they do not appear to be leaking.
Where else could there be a leak? (floor is dry)
It won't be the gasket between the tank and bowl.
My guess is if it isn't the flapper inside, you probably have a crack in the plastic flush valve assembly. It's that white stand pipe the flapper is connected to.
I haven't seen a brass flush valve in a long time. Is cheaper better?