I have a 1997 F-250 HD with the 351W and E4OD. I've recently developed a chirping noise coming from what sounds like the transmission. A little while ago, my transmission cooler line had a leak, so I leaked a lot of fluid. It leaked enough where very little showed on the dipstick at all. I drove it when it was low for a little bit, then this chirp developed. Even after filling the transmission to the proper fluid level, it still makes the noise. Currently I have found it only makes the noise under these conditions:
-The truck must be in drive. It will not chirp in park/neutral. If i go in neutral while driving, and while it is chirping, it immediately goes away.
-It will not chirp if I have a very light load on the truck. Meaning if im going light enough on the gas pedal, the chirp wont happen.
-It also won't chirp if I'm not moving while in drive.

Because of the conditions of when it chirps, I suspect it could be a transmission problem. Any ideas on what it could be? I'm stumped.
And yes, I am sure it's not a belt. Its been replaced

 

Where do you find it appears loudest? Front, rear, driver side, passenger side,inside or under the vehicle ?

There are several components that make up the drive line and most can be checked visually, while some may need to be disassembled to prove to be the source.
The idea is to list the conditions that are active when the chirp appears and check them ALL, one at a time.

The drive line includes the wheels also !