My guess is that the wood pores are filled with the old finish that penetrated and sealed the wood.  The only way you'll get more color is to build it on the surface, rather than penetrating it into the wood.  It's hard to get it on even by wiping it on, and it takes forever to dry.  I have good luck using my HVLP turbine spray gun, and cut back the stain about 50/50 with acetone or lacquer thinner.  Spray outside with good air flow, to avoid the fumes and the possibility of a static discharge explosion with the volatiles.

The high volume air flow, along with the volatile carrier, causes the stain to go on almost dry, and you can control the build-up to get the shade you want.  This technique is also good for woods that take uneven stain, because you can build up the light areas more to get even color.

I am a professional antique furniture and wood restorer and I can say without hesitation that the stains and clear finishes sold in hardware stores and box stores are worthless garbage. Nothing but chemicals and plastics that wood hates. I don't know what species of wood you're working with but a couple of cheap formulas that you can easily make yourself are as follows. Buy a bottle of vinegar and a bottle on ammonia. Put the vinegar in a screw top container and toss in a bunch of rusty metal, nuts, bolts or what have you. Shake it up once a day for a week or so and you will have a stain that will give a beautiful chestnut color to most woods. More stain deeper color. With the ammonia do the same thing but add used coffee grounds instead of rusty metal. This will give a nice walnut color. Be careful with the ammonia because on some woods there will be a chemical reaction that you don't want I.E it will turn cherry black as ebony. Rub out the wood with a fine abrasive after each coat as it raises the grain. For a finish it  depends on your preferences. Nothing can beat a high grade of Linseed oil for beauty and durability but it takes time. The rule is one coat a day for a week, one coat a week for a month, one coat a month for a year and one coat a year for the rest of your life. You can use the rifle while you are doing this, thin coats well rubbed in. The other choices are the varnishes. Shellac is orgainic, easy to use, looks good but scratches easily. A long oil varnish is the better choice and is what most of the gun companies used after the war. Don't confuse this with the polypissethene varnish from Min Wax etc. Other than from small specialty makers it's hard to find. Macluskey Man O War is the only commercial one still available to my knowledge but they may have changed it. I make my own but that is a different story. My rule in my work is to ask "How did they do it 150 years ago"? The answer is usually the best.  Good Luck

I took it down to bare wood with 100 grit and then went back over it with 220 grit. It  had been redone before I got it l could tell from the barrel channel and a little on the buttstock.

I have had great success with Fiberings leather dye. It will penetrate!

1Hawkeye,

Since you sanded away the old finish, I suspect that there is still finish in the wood.  You might try lifting the old finish with paint remover to see if it improves the ability to accept stain.

According to the old ads for the BSA internationals the wood is French walnut. But I've never had wood act that way with stain regardless of the species and I was definitely down to bare wood. All I could think of is that as some woods age they get harder and this is what may have been the case. It looks pretty sharp on the barreled action I was just wanting it a little darker.