My toilet has an old-fashioned solid brass ballcock for a fill valve
rather than a more modern pilot-valve fill valve. It has started
leaking just a little, so after it shuts off the tank continues to fill
*extremely slowly* until it spills over the overflow pipe.

I actually like this type of valve better than the Fluidmaster type
valves that slam when they shut off. I have quite high water pressure
and the modern valves are noisy and don't last very long.

Do I just need to take brass valve apart and clean the seat? Or is
there more to it than that? I don't think this has a rubber washer
inside; I believe it has a metal-to-metal seal.

Bob