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Short version: does two-stage thermostat always close W1 circuit when it closes W2 circuit, or they might be closed independently?

Long version: I have two-stage furnace, currently connected to older thermostat with single W wire, so thermostat's W wire is connected to furnace's W1 wire.

Furnace also has a small water pump which pumps water generated by furnace when it is working, it is plugged sequentially with thermostat's W wire - so when furnace is ON, water pump is ON too.

Now I want to add new thermostat with two stage support - so I'll have W1 going to W1 and W2 to W2.

The question is how should I plug water pump. If I plug it sequentially with W1 as it is now - will it work? My worry is if thermostat might close W2 alone - in which case it will turn on furnace without turning on water pump.

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