I think you're answered your own question re the unconnected coiled black wire, sounds like it does nothing.
12V circuits don't usually have separate commons and grounds because the voltage involved is not a shock safety hazard. So most likely you will just be connecting the wire with the 3A inline fuse (which ought to be +12V) to the +12V terminal of your new switch and the old "common" (which ought to be -12V) to the "ground" terminal of the new switch.
However, there is much confusion on color coding of 12V circuits in RV's because sometimes things are wired using automotive convention and sometimes household ac wiring convention. IOW, you can't really trust the color codes. So, get our your trusty digital multi meter and test the polarity of the two conductors you're connecting before final hookup.
If you don't already have a DMM do get one, you will use it often checking various things on your trailer.