If the button is square and it should push in easy, and is spring loaded, the rod will just fall out. The cleaning rod is held in by the button latch that hooks onto a notch on the rod. The Type 99 rod does not screw into the stock, rather it just falls down in. Use a coat hanger wire and see if that fits inside the hole about 20 inches or so. If not, something is blocking the hole. Are your stock screws still staked and in place- never taken down after the staking -- that is good for value, but bad if trying to get the hole cleared. Keep it in the stock & no refinish.
Ok as a trial case, I took my .22 rod and pushed my button down and my .22 cal. rod went in the cleaning rod hole to a depth of 21 1/4 inches. So you have an obstruction or the stock was switched and you have a late war stock?? Highly unlikely due to your square button. If your screws have been turned and are no longer are staked in place, you can take the action out of the wood without hurting the value. Try upside down and see if anything falls out, or use a tiny wire with a flat tip to sort of drill into the blockage and see if it's mud, wood, or metal. You can tell by the dust/chips that come out.
B & W in poor light
Square button to push down
notch on original rod that the button snaps onto
Intact staked screw
Chrome bore ring
aircraft sight with wings
To old to fight and to old to run, a Jar head will just shoot and be done with you.