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I would clean it up and carefully examine the gear contact surfaces. Also, carefully check for cracks in the posi case, particularly emanating from the corners of the “windows”.
Check the backlash and the pattern. You will need a dial indicator and base for the lash and some marking paste for the pattern.
Measure the axle sideplay.
Make sure the ring gear bolts are tight.
If you have access to an in-lb torque wrench, measure the preload torque.
As gtr1999 recommends, I would replace the pinion seal and side seals.
Knowing what you have now will give you confidence (or concerns) about the expected longevity of the unit.
Once you are satisfied, fill it with Lucas 85-140 and two bottles of Delco 10-4003 additive.
I just took a break for a moment. Can you rotate the posi and take a closer picture of it showing the cross shaft hole and back window? The picture I commented on was not as clear as your second one and there's something I would like to see clearer.
I guess our timing was off. In the picture mentioned the tooth count was for a 370 as noted. The date code is Sept 1978. The diff was apart at some point as there is a witness mark on the cap and housing, but what I couldn't clearly see is the posi case OD. It appears in the close-up picture to have impact marks from the pinion at some point- could be the reason why the diff came apart. If the preload is too loose or under hard launch, the pinion will move rearward.
I am not saying that diff has a problem, just that it has been apart for a reason. I hope you don't have any issues and enjoy the car.
It was opened up so thats true that it was opened for a reason. I took her for a drive yesterday and she seemed solid. I did not hear any noises or vibrations. Hopefully it will stay that way. Thank you all for the help, special thanks to GTR1999