If the tube runs above the front window (or anywhere up high in the front, it's a fairing tube for the purpose of providing a path from the thermometer readout down to the sensing bulb, which was located on the belly pan street side just aft of where the tongue meets the skin.
Your electrical questions have me stumped. I would guess an alternate use for the switch--it selects between getting 12 volts from a converter or the battery. One reason would be to prevent those old converters from fighting with your car 12V
connection and its charging current. But that's just a guess.