you lucky, that one does have an online parts breakdown, most mid 1960's and older do not and you have to dig in the old books.
Partstree is the easiest to navigate ( I recommend using a laptop/computer to navigate not a smartphone) the main page shows the parts explosion pages for the main engine to find part number from and the three listed underneath under "attachments for this model" are for the magneto, recoil starter, and carburetor parts that came on that particular engine.
not affiliated with partstree nor do I order from them, they just have the easist to navigate for me parts lists setup that is supplied by Tecumseh to vendors to view.......they say they have something, take your money, and then might kick it back, so I just use the part numbers to search old stock etc with other vendors and shops I use.
https://www.partstree.com/models/h22-15030f-tecumseh-engine/