Chunger, it's not uncommon to find Spencers missing inspector cartouches because so many of the stocks were refinished by subsequent owners, and many of those refurbished by the government often had older cartouches removed and new ones added. If the specimen carbine you are looking to buy is "sterile" except for the maker's identification and has no letter stamps on the left side of the barrel next to the frame, or on the left side of the rear of the frame, or the tang of the butt-plate, or on any internal parts, then it may not have been inspected by the government inspectors? But if it has these "letter" stamps on the major assemblies, and no inspector's cartouche stamped in the stock behind the sling staple, if the metal is higher than the wood then the stock has likely been sanded, and the cartouches may have been removed.
Only if you know the full provenance on a particular rifle or carbine can you possibly know when any such work was done, and too many of these guns have no known provenance. The M1860 Spencer carbine government contract of 1863 was extended up to September 1865, and they took all the factory could produce until the end of April 1865 when the order was cancelled, though deliveries continued until September. Just to give you some idea of when other M1860 carbines were issued, 31519 and 31522 have been identified as issued in July 1864, while 52371 was supposedly issued in March 1865, and 56722 in May 1865, so chances are the 36,000 series was probably delivered in the fall of 1864.