Hello, what you need is John Deere Corn Head grease. It has the NLGI rating of 0 (ep-0) I have a tube in the garage. I used it for the steering box on my tractor with great results. It is made for steering boxes and gear boxes. It will not leak out of old seals like gear oil.
The following table shows the NLGI classification and compares each grade with household products of similar consistency.
NLGI consistency numbers: 000 445-475 fluid cooking oil 00 400-430 semi-fluid apple sauce 0 355-385 very soft brown mustard 1 310-340 soft tomato paste 2 265-295 "normal" grease peanut butter 3 220-250 firm vegetable shortening 4 175-205 very firm frozen yogurt 5 130-160 hard smooth pate 6 85-115 very hard cheddar cheese