I use Amsoil 75-90 gear fluid.
Been running it since new.
There is a pump in these T-cases, but with a synthetic, works great.
Took it apart at 85K miles when I installed my DTT transmission.
Had it out, and figured why not check it for wear.
That was a waste of time. Was clean as new inside.
Even the magnet wasn't worth cleaning off.
Put some more of the same fluid back in.
Brad