What condition are your leaf spring bushings in?
Might sound unlikely, but it can get pretty bad. Mine have been squeaking occasionally, & sometimes they are worse. I've been meaning to get some poly replacements, but OBA & on-board welder have kept me occupied recently.
Since this is cheaper than driveshaft/t-case/diff repair, I'll go ahead & hope it's the front eye bushings of your rear leafs, for you. Good luck!