I had the same "musty" problem with the antique sewing machine that I bought a couple years ago. It has wooden drawers, and they were horribly musty. ...I'm trying to remember what I did to get the odor out....
Oh yes. I somehow got the notion to use boric acid on it. It was a horrible mess! LOL. I'm not sure how much it helped to tell the truth. If I were to do it again, I'd probably wash the thing down with a baking soda in water solution, or a light bleach solution.
What definitely did help, was that I followed up by oiling it with high quality furniture oil. I used tung oil, and I wonder if it may have had an anti-fungal quality, because there's not a trace of mildewy smell now. Tung oil has a strong smell, but not a bad one, and it fades. In any case, the wood looks great, and loved the oil...and no more smell!
KnittingHelp Queen Bee
"There is a vitality, a life force, an energy, a quickening that is translated through you into action, and because there is only one of you in all of time, this expression is unique. And if you block it, it will never exist through any other medium and it will be lost. The world will not have it. It is not your business to determine how good it is nor how valuable nor how it compares with other expressions. It is your business to keep it yours clearly and directly, to keep the channel open. You do not even have to believe in yourself or your work. You have to keep yourself open and aware to the urges that motivate you. Keep the channel open."
— Martha Graham