Someone needs to use a test meter to confirm whether this is a "power available" indicator or perhaps a ground fault in the
boat and a
danger. If you're not familiar with the
electrical system and with AC
safety procedures, a trip to Vegas, ergh, finding a good electrician, might be in order.
Stray AC
current can kill people and burn down
boats, so yes, you are absolutely right to worry about why "off isn't off" type stuff.