I mentioned this above, it does not conduct. Overlapping puddle zones are not considered one puddle, but if you place The Big One in a spot that both puddles are touching they’ll both get shocked.
As an example of where this won’t work, go to Dalia’s bathroom and turn both sinks on, then throw The Big One into the dry strip between the two. Neither puddle should be shocked. Now go to the bathroom on Hokkaido and try it and you’ll see the two sinks are close enough that their puddles overlap. Throw it in the middle and it will shock both, but throw it on the left/right sides and it will only shock one of the two even though the water appears to visually be one puddle.
I’m 99% sure that turning on a sink instantly and automatically generates a “puddle zone” that the visual effect slowly fills out, and it only goes away if an NPC cleans it up completely. The zone is what matters, not the visuals. If a zone is active it can be shocked, if it isn’t it can’t; shocking is a one-time event that occurs when a person either touches an electrified puddle or when electricity is applied to a puddle in a single action (turning on a plug, The Big One effect, etc.). On some maps there are preexisting puddle zones (the shop on Landslide e.g.), but unless something is defined as a zone it can’t be shocked which is why the shower and spa on Hokkaido don’t work.
EDIT: I would also guess that the puddle zone is a perfect circle, basically just a radius from the puddle generation point. That’s why you can shock people who seem to be standing on the edge of or even outside of the puddle, as the visual puddle shape is different for different sources (sinks appear more elliptical in their puddle projection but this isn’t accurate).