Grease needs to 00 or 000 grade, anything else will just get pushed to the sides and the box will run dry. 00 or 000 grease will flow back on to itself, or what is called self leveling. 1/2 gun grease and 1/2 gear oil will work once premixed. Corn head grease is 00 grade, made for slow speed gear boxes.
I would recommend cleaning the box inside and out, even if there is no movement. Pull the side cover and flush with gasoline or your cleaner of choice. There are roller balls, bearings, and bushings that could use some fresh grease.
Just follow along in this manual,
https://www.flickr.com/photos/advance-design_parts_co/sets/72157632210242370/ , the boxes are very similar. You will be surprised how much better the gear box will feel with a fresh overhaul.
Joe