Need a circuit that can switch motor direction by photo or timer input

What you have there is an engine coolant fan from some sort of VW vehicle.

According to page 97-940 of the VW Jetta/Golf/GTI 1999-2005 service manual published by Bentley Publishers, brown-black and red-black go across the motor, and red-black and red-white go across some sort of resistive sense device, possibly some sort of thermal device. I can't supply an image of the service manual, but the fan is either device V7 or V35 on the aforementioned page.

The fan itself is meant to be connected to the coolant fan controller (J293), but unfortunately I have no further information on said device.

On any individual circuit (lamp or 120V outlet) the current in the neutral in that circuit is equal to the current in the "hot" wire.

If you have equal loads between black and neutral, and between red and neutral, the "black" current and the "red" current will cancel in the neutral - there will be no current in the shared neutral wire.

Anything that only uses 240V (hot water heater?) will not connect to the neutral, and therefore will not cause any neutral current.

An electric stove will use 240 V for the heating elements, but also uses some 120 V for lights and a clock, so will require a neutral connection, and so will generate some neutral current.

The current in the neutral wire between your house and the power company's transformer will depend on how the loads in your house are balanced between the two "hot" wires.