Would like to have the ability to not have a tag icon at all. If I keep this setting with a blank field, there is a default icon, still.

Having the blank field selected means that when you add a tag by right clicking, no icon is selected in the pop-up.

What the game does if you add a tag with no icon, is to use his own default marker. That is the case with my mod and with vanilla.

I can't find any issue with the setting itself, so I suspect you meant the default marker, and I can't remove that one.