Airstreams suffer from interior humidity similarly to boats with living quarters such as sailboats, cruisers, houseboats, etc., due to the impermeability of the aluminum construction which does not allow the exchange of atmosphere.
Those with interior aluminum walls have condensation-issues...those with fabric or "mouse fur" develop mold-spots...which is likely what you have rather than water leaks (although that is a possibile contributor.)
When we bought our used AS we thought they were use-stains but soon realized it was mold. I fixed it with a shop wet/dry vacuum and a product known as "Spot Shot" found at WalMart. https://www.amazon.com/Spot-Shot-009...478974232&sr=1
I spray the aerosol product onto the stain and as the spray is advanced along the stain the spray is closely followed by the vacuum hose/adaptor. Thereby the stain is hit with the cleaner and immediately, while still wet, sucked up along with the stain.
Works great and no further mold development (probably since I don't store the unit outdoors all closed up like the Previous Owner did.) Some folks store their units with a dehumidifier inside and periodically empty the dehumidifier-pan...and some folks put the DH inside the shower so that when it overflows it simply runs into the grey tank. (I don't use a DH at all as I live in a fairly dry area of the world, Central TX Hill Country, and I have it stored inside a dry bldg.)