I would use the gear oil but first have a look at the brass gear with a flashlight to make sure it is not chewed up.

Looks good there was still maybe 2 oz of lube in there. I sucked out the old fluid, man it was black! Filled it to the bottom of the fill hole.

I'm sure that you will watch over your oil level. If it starts going away, your choices are rebuilding the box or draining and re-packing it w/grease. #2 lithium goes in some boxes from new.

Seems to be keeping it's lube well now. Hope it continues this way.