What the local weather actually does to these walls
Hermosa Beach doesn't get much rain, but it gets a lot of marine layer. Morning fog rolls in for months at a stretch, spring through early summer especially, and it pushes moisture into stucco, into old wood siding, into any gap around window flashing. That moisture doesn't need a storm to cause trouble. It seeps in slowly, night after night, and shared walls near the ocean side of a property take the brunt of it because the fog sits heaviest closest to the water.
Add to that the salt air, which speeds up corrosion on flashing nails and pipe fittings, and you get failures that are gradual rather than sudden. A damp patch that's been building for a year from fog intrusion looks different from one that showed up after last week's rain. The slow one tends to be wider, with a soft edge and sometimes a faint white mineral bloom (efflorescence) if it's coming through stucco or block. The fast one is usually more defined, often lower on the wall if it's plumbing, or up near the top if it's roof or parapet related.
Buildings from before the 1980s in Hermosa Beach often don't have a real vapor barrier in the shared wall assembly, so moisture can migrate sideways through a stud bay and show up on your side even though the source is on your neighbor's plumbing or exterior.
More on this from How To Tell Whose Side A Damp Patch On A Shared Wall Came From.
What you can check yourself before pointing a finger
Start by mapping the patch against your side of the wall. Is there a bathroom, kitchen, or laundry hookup directly behind it, on either side? Pull up any accessible cabinet fronts nearby and look for warping or a musty smell that's stronger than the room around it. Check your own roof, gutters, and any exterior wall penetrations, hose bibs, dryer vents, AC line sets, since a bad seal on your side can absolutely cause a stain that shows up looking like it belongs to the neighbor.
Look at the exterior too. Walk the outside of the shared wall if you can access it, and check for cracked stucco, gaps around window trim, or a downspout that dumps water right against the foundation near that wall. In a lot of Hermosa Beach's older housing stock, cracked stucco from settling is the single most common entry point for fog moisture, and it's often nobody's obvious fault, which complicates the whose-side question further.
Where guessing stops being useful
Visual inspection tells you where the stain is, not where the moisture is traveling from, and those are frequently two different places. Water can enter high and travel down inside a stud bay, or wick sideways for several feet along a horizontal framing member before it ever shows on drywall. This is where air quality testing and moisture mapping earn their keep. A thermal camera combined with a moisture meter can trace the wet path through the wall cavity without opening it up, and it can usually show which side of the party wall the moisture concentration is heaviest on, which is close to proof of origin even when it isn't perfectly clean-cut in a shared assembly.
If mold is visible, or if there's a musty smell that persists after the surface dries, that's the point to bring in someone who does indoor air quality testing specifically. They can sample the air on both sides of the wall and compare spore counts and types, which is genuinely useful evidence if this ends up being a conversation between two owners or two HOA units about who fixes what. It also matters for your own health and your kids' or tenants' health long before it matters for who pays the contractor.
Getting to a fair answer with your neighbor
Most of these disputes resolve better with data than with opinions. If you can show a moisture map or an air sample report that points clearly to one side's plumbing or exterior envelope, that conversation with your neighbor goes faster and with less resentment. If the source turns out to be a genuinely shared element, like a party wall parapet cap or a downspout serving both units, that's usually a shared repair, and knowing that early saves both of you from a longer argument.