Bypassing switch on electric drill. Which way to wire field coils
The two field coils must be connected with each other such that if DC were to be applied, one makes a north pole at the surface of the rotor and the other makes a south pole at the surface of the rotor. You could test that by actually applying a low dc voltage. If you test it with AC, I believe the motor will vibrate rather than turn its the connection is wrong.

If the field coils are connected wrong with respect to the commutator, the motor will turn in reverse.