The transmission/hydraulic fluid for these and most older tractors is called UTF, Universal Tractor Fluid. When yours was built, Yanmar specified 'John Deere 303 or equivalent', a single-grade fluid aka J20A. Both specs are obsolete. For today, Deere spec J20C is multigrade UTF and a better spec.
There are UTF's sold today labelled '303' but because there is no specific formula for 303 these are reputed to be the worst quality of UTF. But they may be equal in quality to what Yanmar considered minimum acceptable back then. I've run cheap 303 in my manual transmission YM240 for years, but J20C equivalent in the Powershift YM186D, which I think is more sensitive to quality. If you aren't pushing that tractor hard in commercial service then any J20C-conforming brand of UTF should be fine.
Edit: Looked in my YM240 Operator Manual: "Use only John Deere Type 303 or Hy-Grad [sic] transmission and hydraulic oil or its equivalent in the transmission-hydraulic system." YM1500 is a few years older so this would have been its original recommendation too.
Deere literature says Hy-Gard should be used when J20C is required, and Lo-Temp Hy-Gard when J20D is required.
Seems to me anything with wet clutches or wet brakes needs quality fluids, but just gears aren't so picky.