you want a Hypoid gear oil. SAE 75W90
found in just about any auto store.
I use Royal Purple brand in my 2000 S.
Got it at Napa but it is a popular brand widely available.
It's gear oil. You don't have to change it TODAY. Order it, wait a few days, do the swap. Pricey, I suppose. But do you want to have second thoughts about putting the other stuff in there?
Besides, it's not motor oil...how often you doing this?