A lot of things are inaudible to this old fart, but locking up in 6th AND the high pitched sound going away tells me that it is not the fan clutch. That cycles on temperature and not the tranny gear. Have you had the truck scanned?
I have a scanner, no codes related to this. Have you watched/listened to the video? The fan cycles up and down really fast (1s/5s), abnormal it seems? And the high pitched squeal is painfully loud, if you can hear it. My kids complain, "what's that noise Dad?"
It all *seems* to be engine RPM related. There is obviously fan cooling at lower RPMs, but the fan is spinning faster when I downshift.