The tung oil will block the penetration of either a water or oil based stain. An alcohol based leather stain will penetrate oil to the wood below but you won't get the same result as applying stain to untreated wood. At this point you would be farther ahead to strip the stock back to bare wood and try again with a dark walnut stain, maybe with a touch of red mixed in.
Garand stocks were not stained as a matter of course. Initial treatment of stocks was by immersing the stock in pure tung oil and letting it dry. Once in service stocks were maintained by applications of raw linseed oil. Oxidization of oils in the wood also contributed to color change. You will see all shades of brown in walnut stocks ranging from light, medium and reddish to dark brown.
For new untreated stocks I use an oil based stain if I want a result other than the natural walnut. When re-finishing used stripped military stocks an alcohol based stain works best to penetrate the residual oils in the wood. Boyds ships their front handguards with a spacer block of scrap walnut installed. You might want to experiment on this with stain to check the color before tackling the stock.
