What you have pictured there is quite different from the domestic Dart instrument panel. That instrument panel is Philco/Ford design. Where our Chrysler panels have copper trace on phenolic circuit boards, our Fords have that same copper trace on plastic film you have there.
The "unit connected" you show attached with 2 button/snaps is the PhilcoFord version of instrument voltage regulator. It does the same thing as Chryslers instrument voltage regulator, reduces 12 volts to approx. 6 volts so their same gauges originally designed for 6 volt systems continued to work in the later 12 volt models.