I also restore antique wood radios. Those were originally finished with tinted lacquer. They did not normally stain the wood separately.
To duplicate it today, the wood is prepped then filled with a paste filler. A thinned shellac seal coat can be used. Then the colored lacquer is applied by spraying. Rattle cans are available from Mohawk. Several coats are done in rapid succession. Flash off time is about 10 minuets on a warm day. Be careful with piling on finish to avoid blushing. The result looks like the rifle above. I have used this technique on guns and it works well. The gloss can be adjusted to whatever you want by rubbing it out with fine abrasive. I tend to use Automotive rubbing compound and Windex. Lacquer is more durable than people realize. Lots of factory guns were finished with lacquer.
I suspect the rifle in question was finished with some kind of varnish with the color mixed with the finish. Nitrocellulose lacquer was not a common thing here at the time the rifle was made. Lacquer tints are compatible with varnish. IF I were to try to duplicate the finish n question I'd use spar varnish with japan dryer, tint, and automotive reducer. I'd spray it. I see no reason it could not be floated on with a soft sable brush. When the color is correct, if the grain is not filled, then go to clear finish. Cut an polish as usual.