So Permatex has several RTV Gasket Makers in different color tubes for different purposes, like water pumps, transmissions, hi-temp, or sensor-safe. The Green one is for gear oil. The Red only says it "resists" oil. The Green says, "
Specially formulated to withstand the harsh gear oil environment found in differentials and transfer cases. Because gear oil has friction modifiers that break down normal RTV and cause leaking, this specialty silicone has been tested to OEM specifications to ensure complete sealing. As a gasket maker, it seeks and seals leak paths that cut gaskets cannot. It can also be used to seal cut gaskets.
That's the one you want. It is Permatex part number 81182. $8.46 on Amazon. Instructions say apply a bead, assemble and tighten only finger tight. After an hour retighten only 1/4 to 1/2 turn. Cures in 24 hours.
I've found the waiting time is really important, lest you end up with the material totally squished out.
Good luck with it and if it works you can say you've got the first "Green" Amel.