Plug into shore power and when it’s real quiet, let you ears find it. You should hear a humming noise. If you still don’t, unplug from shore power and then turn on several lights to run the battery down a little. Now that the battery needs to be recharged, plug back into shore power and listen closely.
According to the sales brochure, many 2006 Ambassador iare equipped with a 2000W inverter. That would also act as the converter/charger and is probably physically located in or adjacent to the battery compartment. You can just follow the battery cables backward from the house batteries until you reach it.