When I turn on my windshield wipers in any speed my windshield washer begins to spray. It sprays continuously until the washer tank is empty. What should I check or change to solve this problem?

If the windshield wipers on your 2002 Corvette won't shut off, it could indicate a problem with the wiper control switch or a malfunction in the wiper motor circuit. Here are some troubleshooting steps you can try:

1. Check the wiper control switch: Ensure that the wiper control switch is in the "Off" position. Sometimes, the switch can get stuck or malfunction, causing the wipers to stay on. Try moving the switch back and forth a few times to see if that resolves the issue.
2. Inspect the wiper motor relay: The wiper motor relay controls the power supply to the wiper motor. If the relay gets stuck or fails, it can cause the wipers to stay on. Locate the wiper motor relay in the fuse box or relay panel and try replacing it with a known working relay of the same type to see if that resolves the issue.
3. Check the wiper motor circuit: The wiper motor circuit may have a short or an electrical problem that is keeping the wipers engaged. Inspect the wiring harness connected to the wiper motor for any signs of damage or loose connections. Use a multimeter to check for continuity and proper voltage in the circuit. If you are not familiar with automotive electrical systems, it is advisable to consult a professional technician or a qualified electrician.
4. Disconnect the battery: As a temporary solution, you can disconnect the negative terminal of the car battery to stop the wipers from running. This will disable other electrical components as well, so it's recommended as a temporary measure until the issue can be properly diagnosed and repaired.

From the 2013 operators manual;

Push the windshield wiper lever forward to spray washer fluid on the rear window. The lever returns to its starting position when released.

The windshield washer reservoir is used for the windshield and the rear window. Check the fluid level in the reservoir if either washer is not working.

Check fuses or washer pump. .replace.

There is a electric motor that pumps washer fluid . Located in the bottom of the washer fluid tank .
Wash Operation (Front and Rear Wipers)
The front and rear washer systems use the same windshield washer fluid pump. When either the front or rear wiper is in the washer position voltage will be supplied to one side of the windshield washer fluid pump (depending on whether it is front or rear), while the other side of the pump is grounded.
At this point, the windshield washer fluid pump sprays solvent onto the windshield. When the front or rear washer is activated, the BCM receives an input from the switch that is activated. The BCM will control the wipers while in the WASH mode. The BCM will control either the front wiper relay or the rear wiper relay to turn on the wipers. The windshield wipers operate at low speed for 3 swipes and returns to the park position.

When turning on the washers do you hear the motor run ? Have some one try it while you listen at the washer fluid tank ! These pump motors do go bad .
turn OFF the ignition.
Disconnect the harness electrical connector of the windshield washer fluid pump.
Connect a test lamp from the windshield washer pump control circuit to a good ground .
Turn ON the ignition, with the engine OFF.
Press the front washer switch.
Does the test lamp illuminate?
YES or NO !

Does the pump motor run when turn windshield spray?
Might be home in line.
Might be wrong fluid(too thick)
Might be wiper fluid motor broken.

Diagnose Turn Signal Problems eHow

Could be - or the pump has failed, or the tank is empty.

Possible there is fault in the cluster switch , possible that the switch is not contacting according to the intended function to power the front washer and rear washer motors.
You need to check the output or using a multimeter the switch continuity of the wiper cluster switch.

This must be due to a defective windshield-washer-switch. Repacement of it is the only way.

• Windshield Wipers Continue to Run When Turn Signal and Windshield Wiper Switch Are Turned OFF

• Damaged turn signal and windshield wiper switch .
• Damaged windshield wiper motor .
• Damaged windshield wiper control module.

Pin Number Circuit Circuit Function 1 57 (BK) Wiper Motor Ground (Park) 2 28 (BK/PK) Wiper Module to Wiper Motor (Park Switch) 3 65 (DG) Wiper Motor Power (Park Feed) 4 61 (Y/R) Wiper Motor Common (RUN) 5 56 (DB/O) Wiper Motor LO 6 58 (W) Wiper Motor HI
Windshield Wiper System The windshield wiper system consists of :

• Windshield wiper motor (17508) (F-type).
• Washer system.
• Windshield wiper control module.
• Turn signal and windshield wiper switch (13K359).

The windshield wiper control module is:

• Located at the instrument panel fuse panel.

The windshield wiper motor is:

• Attached to the cowl top extension (021A36) .
• Connected to windshield wiper mounting arm and pivot shaft (17566) .

The turn signal and windshield wiper switch features a:

• Rotary wiper switch.
• Push type washer actuator.

OFF/Low/High Speed

• Has a two-speed, permanent magnet, three brush electric windshield wiper motor .
• The windshield wiper motor has a brush rigging that permits selection of low or high speed.
• When the turn signal and windshield wiper switch is in the LO position, the common brush and the blue/orange wire brush are used, and the windshield wiper motor operates at low speed.
• When the turn signal and windshield wiper switch is in the HI position, the common brush and the white wire brush are used.
• In HI position, electric current will bypass a portion of the armature winding causing the windshield wiper motor to operate faster.
• When the turn signal and windshield wiper switch is moved to the OFF position, the windshield wiper motor will continue at low speed until the park switch outer contacts open.
• When the park switch contacts open, the windshield wiper motor stops in the park position.

Interval
When the turn signal and windshield wiper switch is in the interval position:

• The wipers make single wipes separated by pauses.
• The rotary switch is on the end of turn signal and windshield wiper switch .
• The length of the pause can be set from approximately 1 to 17 seconds.
• Length of pause decreases as the rotary switch is rotated away from off.
• Length of pause increases as the rotary switch is rotated toward off.

While in the interval wiper mode:

• It is normal to hear a slight click at the beginning of each on/pause cycle. NOTE: When using interval wipers, the first wipe may not occur until after a pause of up to 17 seconds.