Mike & Keoke could both be technically correct.
A lot of small motors were "series wound". The armature & field windings are internally connected in series. When the polarity applied to one winding is reversed, the polarity of the other is automatically reversed also, so the motor runs the same direction with either external connection. IE. The original Healey fan motors.
Most newer design fan motors, such as electric radiator fan motors, have a permanent magnet field instead of a field winding. These motors ARE polarity sensitive & will run either direction if the connections are reversed.
It's a little hard to know which specific type of motor is installed in an older car. Modern replacements for "old design" series wound motors have been known to have had the design converted to permanent magnet types. Permanent magnet motors are cheaper to build & possibly more reliable.
There are also brushless permanent magnet motors which replace the brushes with electronic switching. These more complex & expensive motors are not likely to be found on low cost applications.
Since it won't damage either type of motor to have it's connections reversed, it's easy to try both connections to see if a change gives the desired rotation direction.
D