I have an H9 rear axle on my new (used) 2004 SCREW Lariat 2WD, confirmed on the pumpkin tag that it is a 9.75. So I know it's a 3.55, with LSD. Guy I bought it fro m did not take the best care of it, though I don't believe it was abused or towed. The other day I was pulling a trailer with about 4K weight total, came to a complete stop with the wheels turned to the right, then turned right when the light turned green. There was some obvious shudder/hop from the right (inside of the turn) wheel as I accellerated, resolve immediately after I was out of the turn.
I've decided to pull the drain plug from the rear diff to see: 1 if there is any metal stuck to it (I assume it's magnetic?) and 2 to check both fluid level and quality.
I've already bought some RP (75-140, I think it said?) to go in, but have a couple of questions...

Is everyone else just using their 3/8 driver extention to open this thing? Mine is an inverted square, 3/8.

What is the electrical line feeding into the top of the pumpkin?

I'm hoping that the original plates just got some friction in 'em after 95K miles of being used very lightly. I've read up on all the diff jobs I can, and think I could tackle everthing except the actual LSD rebuild (don't have that sophisticated a tool set). The Ford Racing LSD's seem to be only 50 or 60 bucks more than the rebuild kit for the one I have, so I'd likely just yank the one in there and replace it. I would prefer to not replace the R+P set unless absolutely necessary.

Looking for any other suggestions/advice. Thanks!

 

Rear axle speed sensor.