It doesn’t say anywhere in the UI that you can duplicate items with the Tower Gloves copycat item.
Whip out the tool glove and set it to copycat.
There to be an option in either this window:
or have it be shown here:
I think for it to be more similar to the other tools, having it be shown like in the second picture would be preferable because that’s how the quick scaler has it:
It doesn’t seem to be mentioned anywhere in the UI.