Richard is correct. They pop out at least 1/4" when they trip and you press them back in (close to flush with the housing) to reset them. - RVs-R-Fun!
The description of the power dropping out... then coming back on its own sounds like a self-resetting circuit breaker might be a part of this circuit. When too much current is drawn, they heat up and open (break) the circuit, just like a regular ci...
It might be worthwhile to confirm the pump itself is working properly. Either remove it and test it or disconnect the input hose from the tank and connect a temporary hose that you know is good. If you are not sure how to do this, many RV supply pl...
Short Simple Answer: A 1,000W Pure Sinewave Inverter should certainly be able to run a 6.5A Max. rated refrigerator... if, indeed, that is the maximum amperage it will ever pull. I hope that helps. - RVs-R-Fun!