It generally takes some time for the reaction to occur, and it can be sped up with a touch of moisture, and a bit of heating/reflux in your collection pot with a condenser on top, or just keep circulating it with the recovery pump. If there is other junk in there you are worried about, you can do a cool recovery distillation (lower pot temperature than you will use during extractions) and/or 13X in the pot after the copper.
You are correct that the copper packing is used in ethanol production distillations for removing sulfur compounds, too. It works best if it is very clean, so if it is not shiny brand new, you can soak the mesh in citric acid water to clean it, then rinse with distilled, shake out excess water and air dry it. The moisture naturally adsorbed to its surface should be sufficient to initiate the reactions in the solvent.