That's a Foote Model 35 gearbox, BTW.
Yep, that old grease has gone off right enough. A semi-fluid grease is what's required - I'd recommend Penrite Semi Fluid Grease, which is NLGI 00 EP grade, and can be purchased in 450g tubes.
A more comprehensive rundown on this topic is here:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php/ubb/showflat/Number/78852/