I have two old circuits with no ground wires in which cables run parallel to each other for 20 feet or so. I had both circuits powered off today and was testing some things for unrelated reasons when I accidentally discovered that my multimeter thinks there is continuity between the neutral slots of an outlet on circuit A and the hot slots of an outlet on circuit B. I took both outlets apart, but couldn't see any wiring anomalies. I also traced the wires pretty thoroughly, but couldn't find anywhere that bare copper could be in contact (obviously I can't see inside the walls). The circuits (seem to) work fine, and it seems like if this were really happening, it would create a short that would trip a breaker. But I repeated the test several times, and the meter kept telling me there was continuity. And the meter has not lost its mind, because it gives sane continuity results in other places where I know for sure what's going on. Could this be some sort of inductive effect due to the lack of ground wires?
Depending on where you're measuring continuity and where the motion sending light is, the motion sending light on circuit could be causing the behavior you're seeing. For example, if the motion sensor is on circuit B (shown as a resistor in this diagram) that can cause your meter to see continuity between the hot on Circuit B and the neutral on circuit A since the neutrals are connected together:
All the neutrals are tied together. If there are devices on both circuits that complete the circuit (light bulbs, etc.), it's possible to measure continuity as you've described.
You'll measure from
probe 1, along the neutral of
circuit A, back to the panel. Then along the neutral of
circuit B, across the load (light bulb, etc.) to
probe 2 on the hot of