The answer to your question is varied. It mostly depends on who installed it. If you have the electrical knowledge, start at the fuse panel and follow the wires. The fatter wires should lead you to the converter as well as the inverter. Likewise, you can usually trace the wire from the batteries back to the inverter.
Another investigative direction - are you checking the appropriate outlet(s)? Not all 110/120 outlets will be supplied with power when the inverter is functioning. You may need to test every outlet to discover which is operating off the inverter and not shore power. A hint, but not necessarily always accurate, is to look for single 110 outlets rather than the double outlets.
A third possibility is the switch isn't for an inverter, but some other accessory like the water pump or water heater if the panel is wired like mine.