Your Argosy has two electrical systems. Your 120 volt AC system (providing “house power” to all your duplex outlets and your air conditioner) is energized when you plug into “shore power.”
Your 12 volt
DC system is powered by your 12 volt battery.
The two systems meet at the converter/charger that plugs into a 120 volt AC outlet.
The converter/charger “converts” 120 volt AC to 12 volts DC and it charges your 12 volt battery. (When it is working)
Your Argosy came with a Univolt. There is no such thing as a good, 40-year old Univolt.
If your battery is dead and if the Univolt is not converting and charging, your lights will not work even if you are plugged into shore power.
Please replace it immediately with an Iota DLS-55 or a Progressive Dynamics converter-charger with Charge Wizard.
Only then can you seriously troubleshoot your 12 volt electrical system.
It's the first thing I do when I buy a new, old Airstream. It was even the first thing I did on our 2007 Classic 30.
P.S. Take no reassurance from a "humming" Univolt. That doesn’t mean it is working.
Hope this helps.