Each flipper coil will have 2 red wires and a EOS switch wire connected to it .

Schematic is a logical representation of the circuit not a wiring diagram. Likely your extra wire is the solenoid power bus that goes to other coils.

When you follow the line upward to the top (red wire), you encounter a T formation at the top. That's the logical representation of the idea that the red wire goes from place to place. In actual wiring practice, the red wire comes "from" a nearby coil to the coil in question, then continues onward "to" another coil nearby, resulting in two red wires ("from" and "to") on the same solder tab. Furthermore, depending on the locations of the coils needing a red wire on one lug, you could have three on a tab to branch off in two different directions, or one on a tab if it's the end of the line for that particular run of red wire.
.................David Marston

The pic is a part of my sticky that folks seemed to find helpful.
https://pinside.com/pinball/forum/topic/em-pinball-circuits-basics-to-not-so-basic

It shows how the physical wiring of a machine does not follow the logical diagram of a schematic.
All the devices physically in the box is connected exactly as the schematic.

The manufacturers connected the wires in the most cost and labor efficient manner, but all the wires in your game will connect to their indicated positions somewhere on the line of the schematic. If that makes sense.

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