I have some new wiring runs and was doing some checking before
connecting to mains when I discovered that a 9V battery was pushing 25
or so micro-amps down a circuit that was supposed to be open, as
nothing was plugged into the GFCI outlets and and lamp sockets were
also empty. This was causing a reduction in voltage due to the battery
being loaded. Looking further, I found that each GFCI (there are 3 in
parallel in this circuit) had continuity from live to neutral and
showed a resistance of about 360 Ohms on a DMM, causing about 120 Ohms
at the end that is supposed to go into the breaker panel. The GFCIs are
made by Pass & Seymour (also says Legrand on the box). Their website
doesn't address this issue. These are their "premium" line and have an
LED on the front. A Leviton GFCI without any LED shows an open between
the live and neutral.

I don't know if all the GCFIs I bought can be simultaneously defective;
or whether the LED or their current monitoring circuit us causing the
continuity. 360 Ohms seems an awfully low resistance to show to 120V
AC. Is the behavior under DC different than AC for a GFCI outlet? Seems
pretty spooky...