Is there such a thing as a switch that can be actuated automatically?
What you are looking for is a rare beast. Honeywell produce a toggle switch (2 position and 3 position) that can be remotely reset by removing the holding current - this releases the magnetic force exerted by a small solenoid and the switch returns to off or centre. This may do what you want but, I suspect that you would want to be able to toggle it at will remotely: -



Why can't you easily find one that can toggle in both directions? Complexity and performance expectations leading to unfeasible cost and therefore NO foreseeable market is the main reason. Hey it was hard enough to find this one let alone one that can be operated at will in both directions remotely.