If the motor has a permanent magnet and just two wires, it will be a DC motor, and will be reversible. There will probably be a rectifier somewhere between the transformer and the motor.
Just connect the motor to a battery, if it spins, problem solved, if not either its broken or intended for AC only.
Motors work by generating a magnetic field in the rotating part which pushes against the field generated by the permanent magnet in the fixed frame. In a conventional motor, the commutator and brushes keep the field shoving the same way. If AC is applied to one of these, it will just buzz a bit and get hot, as it is trying to turn one way then the other in sympathy with the supply. Some motors have a field coil which replaces the permanant magnet. These work on AC and DC, but only turn one way. Some motirsa have the magnet rotating, and the coils fixed and a cunning arrangement of electronicery to arrange the forces to make it all work.
Yours is probably the ordinary permanent magnet brushed motor, as they are the cheapest to make