The picture you show from the shop manual looks to be a smaller diameter fuel pump for a standard V8 engine, not the R-Series engines. Most likely the writers of the Studebaker shop manual did not update this or other photos or diagrams when the Avanti came out. The picture posted on the DeadNutsOn website shows three valves and springs, but I can assure you that you only use two valves, rubber disks and springs and the kit, if I remember correctly, comes with the needed two internal valves and springs. Maybe some of the Carter X fuel pumps use three valves in some applications, but not all.
And when I searched on eBay for "1963 Avanti Carter fuel pump rebuild kit" the same type of kits show in my search results at nearly the same or high costs than the link I posted above. If you should get a rebuild kit for a standard Studebaker V8 fuel pump, that will not work because the diaphragm and all the internal parts are smaller than on the Carter X pumps.