I use NLGI "00" for this reason, and recommend the Tractor Supply option as it is readily available and reasonably priced.
Caution, STP does not contain any anti-wear additives, it's just a long chain polymer (finely ground up plastic) in a base oil. Most #00 grease should contain at least a modi*** of anti-wear additive, if not extreme pressure. That's what I would use. This looks good: https://www.napaonline.com/en/p/SME706612
John Deere Special-Purpose Corn Head Gun Grease Features: Formulated for John Deere corn head and other slow-speed gear cases -30 to 330 F (-34 to 165 C) Extra-soft grade of lubricating grease, required for row-unit gear cases of John Deere corn heads Service rating: NLGI grade 0 JDMJ13A5, J13E6, and J25A Physical properties: Green color Contains extreme-pressure additives Excellent at high and low temperatures Resists moisture and water washout Polyurea thickened Contains anti-rust properties 14-oz. tube compatible with most grease guns Also available in 35-lb pail
I had both corn head and Tractor Supply "OO". I decided to go fill my '32 box with corn head. Ran it all summer and only the tiniest drop leaked out after running the car for two hours. Header runs near box and is not wrapped. The box is stock and does not have modern seals installed.
John Deere Corn Head Grease is the best lube to use. It is thixotropic. Read about it here. Corn Head Grease Use - The Ford Barn