Often it is not connected to anything. However for some it may be for the
propane solenoid switch on US boats, or the owners have attached another device to that circuit such as additional fridge
bilge pump. spot light etc etc.
If you have a
battery monitor you could try switching everything else off, then watch the
monitor as you flick AUX on and off, that might be a clue that it is wired to something that is permanently on or in standby mode, like a stereo system, TV
antenna booster etc.