I having a similar problem. I have a 2003 f250 7.3 turbo diesel. I have a screeching sound from engine compartment Sounds like starter grinding when you start while already started or hold the key in starting position too long. It’s horrible and really loud. It happens when I am parked (stationery) and shift into reverse or in drive and shift back through reverse back to park. Only makes the sound when I have it in reverse. If I shift to another position it immediately stops but it continues for 10-15 seconds when I shift back into reverse again. It is intermittent but seems to be happening more steadily. Lasts for like 10-15 seconds then stops and doesn’t do it again until I shift out of reverse and back into it again. I also have the overdrive light flashing which is new also. Nothing else unusual. I recently used 4 wheel drive. It’s winter in New England and the roads are seriously bumpy. I am thinking something got knocked loose. I have had lots of starter issues but I have a new starter. I am wondering if it’s a transmission issue but I sure hope not. I am new at this and learning so I hope I explained it good enough to come up with a few options to look at.

I read and posted this During the night or early morning hours. I have several ideas that turned up from the handy search function! Lol 😜 Going to check it out today! Thank you