I got an oil from eBay that is similar in size to the M1 carbine oiler. I assume this stores inside the butt stock. There is a lot more room.  I see some sellers offer a sectional cleaning rod with the same oiler. What else goes in there? The cleaning rod?  My gun was made in 1902, if that matters.

I expected to see a makers mark on the oiler cap. It looks old, but; is unmarked. Is that correct?  The seller guarantees real and if all is right, I would go back to him for what else I need. Calls himself Gandpa's Gun Parts.