Hi
Ok,
12V wall wart:
This side plugs into a power outlet that is wired to shore power
---- or ----
Power cord for wall wart plugs into the same place
---- or ----
Power cord gets plug chopped off and wires stripped.
Wires go to shore power inlet.
Once any of those things are done, the wall wart will fire up when you have shore power. It will put out
12V DC or
12V AC (both will work) depending on which one you bought.
Now you take the output cable coming out of the wall wart and cut off the connector. Strip the cable. Solder one lead to each side of the bulb.
Takes longer to describe it than to do it. Sorry about that
Bob