You are right, that normally two wires comes from the motor. But you are not right, that each of the two wires normally comes directly from the brushes. It is an universal motor or series motor, so stator windings are connected in series with the brushes (rotor). In most cases the stator windings consist of two windings to produce the "static" magnetic field of the motor. I guess that some parts of the connection to these windings is taken out to terminals on this motor, because it may make it easier to test the motor windings from outside.
This motor looks very old, and I am not sure that I would use it, because the insulation material of windings of the very old motors are not that good. You may have a professional person to check the insulation by some high voltage insulation test. You can buy new motors and also newer vintage ones.
On newer motors, you can have some EMI filters or capacitors connected to the motor or assembled nearby. They are used to reduce radio interference to older AM radios and old lower frequency TV signals. I do not think this is the case with this motor. But such capacitors can make connections to both sides of the pedal wires as well.