Hi toverman. Welcome to Air Forums where a lot of advice is offered and is absolutely free!
Airstream plumbing systems change through the years. Most of them have circuits in them to help drain the water system for winterizing. You didn't mention the size of the hoses that are leaking. I wonder if they aren't 1/2 diameter or so.
There may be a ball valve or maybe a gate valve that can be opened to help drain the system. Maybe such a valve is partially open or leaking internally. If it only happens while pressurized on city water, and not on 12v
pump water, then look for a valve somewhere near that hose.
Part of the fun of these old Airstreams is figuring out how they were built and how they work. You may have to look in cabinets and closets to find this drain valve.
By the way, Airstream's idea of a valve and drain hose on the "lowest" part of the circuit is not a guarantee all the water is out of the trailer. There is nothing like compressed air blow and then filling the system with RV antifreeze for proper winterization.
Maybe some other Sovereign
owner will further diagnose your "drippy hose" pain.
Some of us would just put a bucket under it and then empty the bucket on the rose bush now and then. Much easier than messing around with some valve.