Shrieking clutch 1996 mustang gt

There is no such thing as an electronic clutch. Assuming your talking about the clutch associated with the transmission. The clutch is engaged via a cable going from the clutch itself to the clutch pedal through the firewall. There is also a clutch quadrant under the dash (attached to the pedal) that is self adjusting. If this goes bad then you need to replace it. What is the issue your experiencing?

I'll assume you mean the switch that won't allow you to start the car unless the clutch pedal is depressed? If so this is not recommended as it's a safety feature. If you disable this the car will move if started in gear and this could be very dangerous.

Otherwise you'll need to look under the dash for the switch. It's in-line with the clutch pedal and it's fairly far up. It typically looks like this:
http://i101.photobucket.com/albums/m44/na93prepre/ClutchSwitch2.jpg

To bypass this you will simply have to jumper the wires together to make the connection as if the clutch were depressed. You'll need to test these with a test light or multi-meter to figure out the proper wires.

check the fluid in the clutch system (if hydraulic) (replace cable if manual). Bleed air out of system replace the clutch master cylinder.

This noise may come from the clutch diaphragm which stops working when the pedal is depressed. The clutch disk might be slipping.

Are you moving a wiring harness under the dash or on the firewall when you move the clutch pedal ?

I had this same problem the cable is fine its a clip on outer cable to stop it mooving when you press clutch mine poped when I tightened the clutch cable still don't have solution though waiting to payday to take it to garage

If theres no damage to the clutch pedal assembly, (no bent fork arms or broken springs), then it sounds like the throw out bearing has gone out.

Worn throw out bearing, replace or the problem may damage other components. This requires dropping the entire transmission. this bearing sits between the clutch pressure plate and clutch slave assembly. When the clutch pedal is pressed, the bearing makes contact with the spinning clutch pressure plate. If defective, grinding/squealing noises may be heard. If the bearing fully fails, loose debris may damage other components. Replace immediately!!

It should have a clutch saftey switch on the clutch pedal.Its a saftey feature simular to a neutral saftey switch it will only allow the engine to crank when the pedal is fully depressed.

sounds like the main shaft bearings within the gearbox itself. i would of said the release bearing but u already changed it. the main shaft doesnt spin with the clutch pedal pressed. check for oil leaks and check the oil level in the gearbox.