This actually sounds strange, since if there is a leak from hot to
neutral, it ought to feed back to other neutral wires which are tied in
to it. But perhaps not, if they are not really making good contact,
just close enough to leak a little current. Did you replace receptacle
itself/ retest? After that, I'd say you have to trace branch. Can you
see the most logical route for it to join rest of circuit? If not, you
may just have to identify all devices on circuit, then by trial and
error disconnect wires at one at a time, recap wires and turn power
back on till you find where branch is fed from. Look for poor
insulation, broken or defective devices. If still no luck, may be
wiring itself- as you say, it's from 50's.
Anyway, keep reading here- others may tell you how to find this more
easily with meter- not my forte.