I did this with a Kokolus reproduction M1903 stock and got good results. I would not do this with an original military stock.
Get a big garbage bag, long enough to hold the entire stock in it. Wrap it tight on the outside with duct tape to reduce the volume inside the bag down. Doesn't hurt to roll up the bag first, as I recall. Support the stock with the open end up, carefully pour RLO until the bag is full, allowing time for air bubbles to escape. Seal it up and leave the stock in there for a good long while to soak the oil--a couple weeks maybe.
To extract, open the bag and pour out the oil. Most can be recovered for subsequent use. Devise some means for supporting the stock, preferably horizontally, and with some ability to rotate, because that stock will drip for a very long time and benefit from periodic wiping. An M1903 stock is easily supported on a length of 1/2" EMT conduit from the buttrap storage area.
Eventually it does stop dripping and cure, and subsequent applications of RLO do not immediately disappear into the wood as happens with a raw stock.