It already should be doing that. It won't output anything if there's nothing to output. This means if the pre-text and post-text parameters are empty and there's no links to display it won't display (either core links or from triggers) the module. What settings are you using within your module? If "CB Plugins integration" is set to "Yes" try setting it to "No" as maybe a plugin is preventing it from being empty.

Which layout are you using under Advanced Options tab? If using horizontal layout it maybe still outputting the span elements. Beyond that try right clicking and inspect element on the module and see what HTML it's outputting to cause it to still display. Even a linebreak in pre-text or post-text could be causing an output.

Try switching to default Joomla protostar template. Seams like it's your template doing it maybe. The module doesn't output the title as that's actually the responsibility of the template. Remove the title and see if the module successfully hides as in my tests this all works fine using protostar template.

CB Plugins integration
for which plugins is this?
which messages the moderator gets here?

CB Gallery will if you've approval enabled.