I'll continue to use NLGI 00 (steering gear) grease, as I have done for 40+ years.

Penrite is a time-honored brand, but not readily available and is relatively expensive.
Tractor Supply - NLG-00 Super Cotton PIcker Spindle Grease at a good price.

John Deere Corn Head Grease is NLGI 0, self-leveling, and a little thinner, and is readily available. It should also work satisfactorily.
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