Greetings Eric!
RE: Water Tank
Your water tank, at least at time of delivery, was in all probability a galvanized pressure unit. I don't believe that the switch to standard demand water pumps with "plastic" tanks occurred until later into the 1960s. The easiest way to find out is to look under the cushions of the sofa bed that resides in the area near the external water fill - - a galvanized cylinder will be the clue to a pressure system that may have a 12-volt air pump to maintain pressure. The presence of a plastic tank will be the clue that the rig has been converted to a 12-volt demand system.
The biggest potential difficulty if your coach has the pressure system is that the galvanized tanks have a habbit of developing pin-hole perforations resulting in leaks at the most inopportune times. It can also take a little more effort to properly winterize as air pressure is a requirement to safely evacuate the water - - and it isn't really practical to consider RV Antifreeze for the tank in such situations. The air pressure pumps are also almost impossible to find new, and rebuild kits can be somewhat difficult to source. One of my friends who has a '60 Overlander is in the middle of trying to source a properly sized replacement pressure system tank for his coach - - the modern replacements are typically too large to fit in the Airstream positions. I have never had a pressure setup in an Airstream, but in my Brand X trailer the guideline was to keep the pressure between 30 and 60 psi - - anything over 60 psi and you could be sure that there would be a pipe separation resulting in 30 gallons of water flooding the coach.
RE: Mystery Switch Behind Sofa
This is likely an aftermarket modification, but I might speculate as to possible purposes. One might be as a power on/off switch for the 12-volt power converter/Univolt(?) - - these were often added to avoid overcharging the battery or to reduce the noise level for sleeping. A second possibility might be to control an optional exterior porch lamp - - these were offered throughout much of the 1950s and 1960s - - the fixture was carried in the trailer and screwed into an outlet on the curbside of the coach - - I have one of these on my '64 Overlander as you can see in this photo:
The switch could also serve some purpose such as controlling some exterior lightling (an assumption based upon its semi-permanent location for the past several years); or could it be a "kill" switch for something like the mini-compressor style refrigerator that has been installed in the coach?
RE: Switches Near Converter
In its original configuration, your coach may have had a city/on-board power switch; the only question in my mind is that it was my impression that the Univolt Power Converter didn't become a standard feature for Airstreams until the very early 1960s - - that could point to an aftermarket addition or a factory option. If your coach has one of the exterior "scare lights", one of the switches might control this light.
Good luck with your check-out!
Kevin