The wiper switch is not very robust, and its failure is common.
I'd remove the wiper arms. Then remove the idler arms from the motor. Try moving those arms. This will give you an idea as to how the mechanism works and it will let you identify any loose joints.
If one arm moves before the other, there is play in the arms.
The motor won't be the problem if it moves the arms. The connection between the motor and the arms is where to start looking.