The post I made was a quote directly from Eaton's reply about what is okay and not okay for use in conjuction with the locking rear end option.

Back in November, I received the following:
"From Mr. Ralph Holmquist of Eaton, the maker of the locking differential:
"The maintenance schedule for the rear axle was developed by American Axle &
Manufacturing and GM truck based on multiple tests. The Eaton locker does
not require additional maintenance nor does it add heat to the lube. The
lube will darken due to the carbon wear on the clutch surfaces, much the
same as a disc brake pad & rotor. This does not damage axle components such
as seals or bearings. However, a new axle can produce excessive
temperatures (plus 350 degrees F) due to the ring & pinion breaking in that
will break the lube additives down. Avoid high loads, trailer towing and
high speed extended driving during the initial break in of the vehicle.
After the break in period axle temps will level at a much lower figure.
Lube changes are a good idea because the additives are replenished and
contaminates such as casting sand are eliminated. The axle is filled at the
factory with a synthetic 75w90 GL5 rating made by Texaco under part # 2276.
The GM service # is 12378261. This is the only lube we have done extensive
testing with to insure locker compatibility. The only negative to using one
of these other lubes is an increased potential for clutch chatter. This
really doesn't hurt anything and can be corrected by changing the lube. I
noticed in the latest GM owners manual the term "or equivalent" when
referring to the lube specification. Look for a GL5 rating on the bottle to
make sure the ring & pinion, seals & bearings are protected. Limited slip
additive is not needed."
The following information outlines the type of
rear axle lubrication utilized in GM Truck axles.
I. Fluid Type
II. The 1500, 2500 and 3500 GMT 800 Trucks utilize SAE 75W-90 Synthetic Axle Lubricant. The GM part number is 12378261 and the specification is 9986115.