That is a new one for sure. Is your washer a Splendide? My washer (a Spendide 2100XC) is 120-volt AC only, no 12-volt connection whatsoever.
Does this happen without any shore power or generator power available, or only when AC power is present? If it only happens when AC power is present, I wonder if (somehow) the washer's power outlet somehow has a relay much like the bunk TVs have to prevent the TV from working when the chassis ignition is on? I do know if my Splendide loses power during a cycle it will come back "On" when AC power is restored.
As far as I know no Senecas have the washer on an inverter circuit from Jayco, any chance someone modified your unit? Possibly installed another inverter that is powered off the chassis batteries and is energized only when the coach power is activated?
2014 Seneca 37TS
Toads: 2019 Ford Edge ST or 2013 Ford Focus ST