Is this a mutual inductor? If not, what is it and how does it work. 
trehill01 Nope. Mutual inductance in the influence of one inductor on another or another conductor in the circuit. In some cases (transformer, magnetic amplifier, etc), it is intentional. In other cases, not so much.
In this circuit, these coils are energized at different time to create directional movement in the valve. It appears as though this is an aviation circuit, balancing / cross-leveling the fuel in two tanks. If either the level or the pressure exceeds a certain level, the pressure or fluid gets distributed to two tanks instead of just one.
A cool example of mutual inductance is a buck or boost transformer in autotransformer configuration. https://www.bristolwatch.com/sr/buck_boost.htm
