The old finish should first be removed - FWIW, I haven't touched a stock I was refinishing with sandpaper in over 10 years - since I discovered Formby's Furniture Refinisher (WallyWorld, Benny's Home & Auto, etc).
Buy a can of Formby's Refinisher, Formby's Yung Oil Finish, and aome OOOO steel wool pads.
Remove the action, etc, from the stock, along with the buttplate, swivels, etc, etc - then simply follow the directions on the can(s).
I pour a little refinisher in a ceramic bowl (recap the can fast, or the stuff will evaporate fast) and dip a OOOO steel wool pad in it to apply the refinisher to the stock. I wipe it off with an old terrycloth towel or am od T-shirt.
Let the stock dry for at least 8 hours, before applying either a dark stain first (Minwax Black Walnut) before the Tung Oil, or just go straight to the Tung Oil. (YMMV)
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