There are a total of five places in the Edit Client pages you can choose to place your new fields. These are identical for both the administration and client pages.
The two screenshots show the options available to you - the locations are highlighted with a blue box. These locations correspond to the "Page and Location" field in the Add and Edit Field pages in the module.
As mentioned earlier, if you're assigning fields to the Settings page for the client, you must have at least one field editable in their main settings page in order for your new extended fields to show up.