Jack,
In England rain does provide natural outdoor light!! Oh ye of little faith, AkA Tung Oil lovers, who continually knock Linseed finishes. Obviously have never holidayed in Britain.
If you are happy with the finish of your stock, leave it for a week to harden in a sunlit window or warm room, sprinkle a little rottenstone over the stock (a pepper shaker is a good tool for this) and then apply a little slackum on your finger and polish longitudenly with care, in about 20 minutes of polishing you will be ecstatic about your stock finish.