The only voltage source for the motor comes from the pushbutton. The pushbutton receives voltage from the ignition switch which also feeds the wiper system so it appears everything is fine at least to the pushbutton as your wipers operate ok. The washer motor has 2 wires, one recieves power from the pushbutton when the ignition switch is on. The other pump motor wire goes to ground. Do you have a multimeter ?. If yes, unplug the motor, set the meter on ohm's and check the Black wire to ground. You should have a reading if it is ok. According to the 99 schematic Brown will come from the pushbutton and will have 12vdc to ground with the ignition on and pushbutton pressed. You can also ohm across the 2 terminals on the motor, you should have a reading, if not the motor is bad. Clear as mud ?
Dave