Everything I've ever done for finishes - bows more than longrifles but my preference for wood in general - is wipe on, wipe off. I don't leave anything soaking heavy on wood for any length of time. Then I just stand it up somewhere to dry.
Stain is not paint. It may be put on light or heavy, but isn't left wet on the surface to dry out. It gets rubbed back removing all excess, before being allowed to dry.
Oil finishes generally are best put on with many thin coats rather than a few thick ones. Put some oil on a patch, spread it around, rub it in, and do not leave excess. Go over the whole stock that way. Leave it a day to dry, possibly steel wool the surface, clean up any steel wool bits, and repeat.
What was that old saying? Once a day for a week, once a week for a month, then once a month for a year? Lots of thin coats allowed to dry between each, generally gives a much better result than a few thick ones. Thick coats of oil finishes tend not to dry for a very long time and can make a mess.
Sunlight helps cure some of the oil finishes such as those based on linseed oil. Hanging so the stock can spin while lit is not a bad plan, if weather etc are conducive. I understand this can greatly decrease the drying time. I don't have that option here. I tend to use the palm of my hand and rub it in until it gets quite hot. I do not leave any excess on the surface. Personally, I don't want any appreciable surface buildup. I want it built up in the wood.
Gerald