If the transmission is caked in oil, then that may indicate you have a leak in the lines somewhere, so you could benefit from a complete degrease and check for any oil leaks.
The following Toro link should take you to page 28 of their Parts and Manuals section where the Groundsman 72 is listed and starts with Model 30720 through to page 30 with Model 30780.
The following are the only Models listed as a Groundsmaster 72 with no additional name/title in these pages, so hopefully, one of them is your machine:-
Model Year of Manufacture
30725 1975
30774 1974-1977
30778 1977-1978
30780 1979-1985
https://www.toro.com/en/parts?Searc...ctedFilterByOption=equipment&page=28I think the best way to help identify your machine would be to provide photos.
The earliest listed Groundsman 72 located above is 1973 model 30720 with serial numbers from 30001 and up called a Groundsmaster 72 Traction Unit. I've provided the link to the Owners and Service manual that has a photo of this machine on the first page. This machine also has the Continental engine R839-46 where the R should indicate it to be a Renault.
https://www.toro.com/getpub/7473Once the machine is identified, then may be able to get the correct manual for troubleshooting.
It's a pity you can't find a Manufacturers Plate hiding on the machine with serial and model number details to make it easier, but the challenge to identify your machine is in progress.
