With second hand shoes, you don't know how the previous owner has taken care of them, using the wrong polish, wax etc. Could be lots of build up. I would start by cleaning them thoroughly with Lexol cleaner, some water and a brush.
My care routine for cordovan is to wipe with a wet/damp cloth, leave to dry and then polish to a shine with a horsehair brush. I periodically use some Saphir cordovan cream.