I have a suggested plan to analyze your situation, but first and most important is that only someone knowledgeable and comfortable with household electricity should do this. No one should accidentally get across a 120 volts, it can kill you and definitely will at least give a shock not soon forgotten. So, please, if you choose to use the analysis technique I describe, make sure that only someone who knows how to do it safely, actually does it.
Now that your new Paneltronics 120 volts AC LED is in the hands of the experienced person, simply find an outlet in your house, the kitchen would definitely be the best choice, as these outlets will be high enough to work comfortably and also will be on a ground fault circuit for safety. As you look at the outlet, there will be a round hole at the 12 o'clock position, and two slotted openings at the 4 and 8 o'clock positions. The 12 o'clock position is the safety ground, which we will not be using. The 4 o'clock slot is the neutral, and the 8 o'clock is hot line. The ends of the LED should be stripped to bare wire, if not remove about 1/4" of insulation from the end of each wire. Now place one wire in the slot in the 4 o'clock position. With the first wire in the 4 o'clock slot carefully slide the other wire into the 8 o'clock slot. The LED should illuminate. If that happens, remove the 8 o'clock wire first followed by the 4 o'clock wire. Now repeat the same process, reversing the positions of the LED wires. The LED should once again illuminate. Now remove 8 o'clock wire from the outlet slot followed by the 4 o'clock wire.
If the LED illuminates in both cases, you have proved that it is non polarized and can be installed on the boat without regard for which of the two existing wires goes to which LED wires.
If the LED does not illuminate in both wiring positions, feedback what happened.
Safety first, second, and third.
Pete