Sounds like you are describing default function of the transfer relay inside the inverter. The shore power passes straight thru the inverter when present. Generator power should do the same. When you say previous owner disconnected... do you mean the 12 volt battery connections??
There should be a circuit breaker feeding the inverter in your AC panel. Try flipping breakers off to see which one kills the microwave power outlets.
2003 34' Dolphin 5342, W22, UP, UPGBrake, F and R Track Bars, Rear IPD sway bar, Koni FSDs, Safe-T-Plus, Scan Gauge II.. 2004 Jeep Liberty, Blue-Ox Adventa..