Removing soaked-in oil from wood stocks

[Wapiti]

Hi fellas,
Just wondering anyone has had success removing the dark oil stains that often are found on old historic firearms with walnut stocks?

I'm referring to oil that has soaked in around action areas from overdoing the anti-rust storage oiling that people tend to do, or maybe it's just because the stocks were never sealed properly in the inletting.

A mate has found a beautiful old 32-20 92 lever gun from the original settling and clearing period in this area, and although the stock on this rifle is original and hardly dinged at all, around the wrist of the butt where the tang is, and the forend around the barrel and mag tube, it's soaked in all this lubricating oil and is just about black.
The rest of the stock has visible fiddleback and grain, and it'd be great to know some ways anyone's used successfully to draw this out and dissolve it somewhat.
Soak in thinners somehow?
Some kind of made-up oil-drawing paste?
He's put it out in the sun and wiped off the oil that comes out and sits on the top as liquid again, but it just keeps on coming.

[straightshooter]

There are two ways to go about it.
Deeply heat the affected areas with a hair dryer or fan heater and then immediately wash off the area where oil oozes out with kerosene but not aggressive solvents like thinners or petrol.
You want the internal parts, as far as there is oil penetration, to be heated without overheating the exterior wood.
Keep repeating every couple of days until no more oil comes to the surface when thoroughly heated.
Alternatively procure some powdered TSP sold as Tricleanium at Bunnings and make a fairly thick paste and apply it liberally to the affected areas and leave it to dry.
You should see a discolouration in the dry paste as the oil is drawn out.
Repeat until no more oil comes out and then wash off any paste remnants preferably with distilled water or rainwater.
Budget a couple of weeks to do a proper job either way.