Hi Sandpirate69,
I think when the slide stops moving the pump continues to try to move fluid, but it has nowhere to go. You'll hear the pump noise change when that happens. I think the pump or trombetta may have a slip clutch, so you may also hear thumping.
Since the pump and switch are using 12V DC, and not 110V AC, the connection to 110V dropping is indirect in some way.
With the A/C on, you must have still been plugged in to shore power. For both A/C and internal 12V lights to go out, I would suspect that the DC voltage to the thermostat and A/C control board dropped low enough for them to malfunction.
It's possible that your power converter has failed or is unplugged. The battery wouldn't have been getting charged and may be low. As the load on the pump increased, it may have sucked up so much of the remaining power from the battery that there wasn't anything getting to the interior of the coach.
If in the past you changed out the 50 amp mini-circuit breaker for something larger, that might allow the pump to draw so much 12V power as to overwhelm battery and power converter.
If you have a volt meter, with shore power plugged in, check for voltage of >13V DC at the battery. That will tell you if you have output from the converter to the battery.
Also check for loose wires, including loose battery terminals, at the pump, and where the battery negative wire is attached to the frame ground.