Spitfire 1500 wrote:

Situation:

I flush the upstairs toilet. It flushes just fine.

About 3 minutes later, the other toilet downstairs does the end-part of a
flush. I can hear the valve downtsairs close(makes a reassuring "thunk"
sound).

Did a little experiment. Flushed upstairs toilet, ran downstairs and watched
the other toilet. The water level in the tank goes down a bit, and it of
course flushes back to normal level.

It's not really "flushing"; the tank is merely refilling itself
and you hear the sound of the water going into the tank.
So it's not a venting issue.

If you have the FluidMaster ballcock (fill valve),
the one with the black plastic float that rides up and down the
"standpipe", they can be very sensitive to changes in the
supply pressure. The kind with the float on an arm made
by Coast Ind. is also sensitive.

In either case, replace or rebuild the ballcock.

Also check that the small "refill" tube does *not* extend down
into the overflow standpipe. If it is down inside, self-siphoning
of the tank can occur which will result in periodic refilling.

Jim