I believe your lights should be 12 volts DC and not controlled by the inverter. To test that theory turn the inverter off and see if the lights still work. Be sure shoreline or generator are not running. If they still work then they are run from the battery.
The inverter may be programmable to "search for loads", and somehow the load on the dc is tricking it into awakening. If that is the case the 16 amps are probably DC amps. That represents about 200 watts of a load. Your microwave should be lit. It is possible your refrigerator is on an inverter outlet and also is drawing some current.
Give some specifics on your inverter and control panel and we can be a bit more helpful.
Myron & Deborah
08 HR Endeavor 40 SKQ
2012 Ford Edge Limited FWD 3.5L
Aluminator tow bar, Demco base plate