What fuse works the windshield washer pump on a 2006 mustang

Replacing parts just to replace them wont fix a bad wire or part. Better to use a voltmeter and ohn meter to check if your getting power to the wires. You may have a bad connection or bad switch on the column for the pumps. Without checking the circuits it will behard to tell what it is thats wrong. Find a wiring diagram and trace the wires and components.

No separate fuse, runs on the wiper circuit. Probably pump bad. If your thinking of doing it yourself, this posting should help.

https://www.ifixit.com/Answers/View/77166/windshield+washer+pump+not+working

There are two relay's in the under hood fuse / relay box . Wiper relay an wiper relay 2 . Maybe one is bad . also check fuse #14 25 amp. Wiper fuse.Plus the BCM - body control module has a hand in making the wipers work . Are you familiar with automotive electronic control modules ?
The Wiper/Washer System consists of the following components:
• Windshield wiper/washer switch
• Body control module (BCM)
• Wiper micro relay
• Wiper 2 relay
• Wiper diode
• Windshield wiper motor
• Windshield washer pump
• Windshield washer nozzles
• Windshield washer solvent container
• Windshield wiper arm and blade assemblies
• Windshield wiper transmission
• WIP/WASH 10A fuse
• WIPER 25A fuse

Wiper/Washer System Description
The body control module (BCM) controls wiper motor low speed operation. The washer pump and high speed operation are controlled directly by the wiper/washer switch. The windshield wiper/washer switch supplies voltage on the signal circuits to the BCM for windshield wiper/washer operation. When WASH, MIST, DELAY, LOW, or HIGH is detected, the BCM energizes the wiper micro relay by suppling voltage to the relay coil. This allows battery voltage from the WIPER fuse to flow through the relay switched input then through the contacts and out the relay switched output to the wiper 2 relay switch contacts. Since the wiper 2 relay switch contacts are normally closed to the low speed circuit of the windshield wiper motor, the motor will operate at low speed.

Do you have any speed !

Hard to say what's wrong without testing thing's . Is there B+ voltage to the wiper switch ? B + voltage to the wiper motor ? Do you know how to use a voltmeter ? How to test electrical circuits ?
Here is a factory service manual list of componets involved .
Wiper/Washer System Components
The Wiper/Washer System consists of the following electrical components:
• Accessory relay
• Heated washer nozzles w/XA7
• WASH NOZ 10A fuse
• Windshield washer fluid level switch
• Windshield washer pump motor
• Windshield wiper motor
• Windshield wiper motor module
• Windshield wiper/washer switch
• Wiper/washer switch 10A fuse
• Wiper motor 30A fuse

Do you know how the wipers work ?
Windshield Wiper Motor Wiring Tutorial
Wipers Inoperative - All Modes ?????
Wiper Motor Switch Troubleshooting

Could be that the switch that activates the washer pump is not closing and that explains why the pump is not working. That has a separate switch from the wipers because you only activate it on demand.

The windshield wiper motor is a smart wiper motor with an integrated electronics module. The internal components of the motor are the high/low relay, washer pump relay, and the run/park relay and associated electronics.
The windshield wiper motor receives its inputs from the windshield wiper/washer switch. These signals are ground reference signals. When the switch is placed in different positions, various input signals are selected and sent through circuits to the motor. The windshield wiper motor module identifies these selected input signals and activates the motor to the selected function.!
Your probably going to need a new wiper motor ! ! ! But you should always test before replacing parts !
Visual Inspection Chart Mechanical Electrical

• Windshield washer pump hoses
• Windshield wiper mounting arm and pivot shaft

• Bussed electrical center (BEC) fuse 10 (30A)
• Smart junction box (SJB) fuse 3 (10A)
• Circuitry
• Windshield wiper motor
• Windshield washer pump
• Windshield wiper/washer switch

• The wipers stay on continuously

• Circuitry
• Windshield wiper motor
• Windshield wiper/washer switch

• Go To Pinpoint Test C .

PINPOINT TEST C: THE WIPERS STAY ON CONTINUOUSLY CAUTION: Use the correct probe adaptor(s) when making measurements. Failure to use the correct probe adaptor(s) may damage the connector.
Test Step Result / Action to Take C1 CHECK THE WINDSHIELD WIPER/WASHER SWITCH

• Key in OFF position.
• Disconnect: Windshield Wiper/Washer Switch C2137.
• Carry out the windshield wiper/washer switch component test. Refer to Wiring Diagrams Cell 149 for schematic and connector information.
  
• Does the windshield wiper/washer switch pass the component test?

Yes
GO to C2 .

No
INSTALL a new windshield wiper/washer switch. REFER to Wiper/Washer Switch in this section. C2 CHECK CIRCUITS 56 (DB/OG), 58 (WH), 61 (YE/RD), AND 63 (RD) FOR A SHORT TO GROUND

• Disconnect: Windshield Wiper Motor C125.
• Measure the resistance between the windshield wiper motor C125, harness side and ground as follows:
  
  Windshield Wiper Motor C125 Pin Circuit C125-10 56 (DB/OG) C125-11 58 (WH) C125-1 63 (RD) C125-9 61 (YE/RD)
  
  
• Are the resistances greater than 10,000 ohms?

Yes
GO to C3 .

No
REPAIR the circuit(s). TEST the system for normal operation. C3 CHECK FOR CORRECT WINDSHIELD WIPER MOTOR OPERATION

• Disconnect all the windshield wiper motor connectors.
• Check for:
  • corrosion.
  • pushed-out pins.
• Connect all the windshield wiper motor connectors and make sure they seat correctly.
• Operate the system and verify the concern is still present.
• Is the concern still present?

Yes
INSTALL a new windshield wiper motor. REFER to Wiper Motor in this section. TEST the system for normal operation.

No
The system is operating correctly at this time. The concern may have been caused by a loose or corroded connector.
You

I would start by checking fuses. If you've checked already, then the windshield washer pump has probably gone bad. The wiper motor and washer pump should be separate units. Typically the washer pump is located in the base of the washer fluid reservoir.

If the pump works, something should be flowing thru the hose to the spray nozzles.
And if the pump works, everything electrical is working.
How do you know the pump works ?

Did you ever fix this problem I have a 03 mustang cobra same problem Please help

Most likely it is the motor, when it failed it likely blew the fuse. The washer pump is separate from the wiper motor. It is also possible that it is the switch.