orthunnus,
In order to display the 3 mile EEZ line you first must be using or purchase a C-Map by Jeppesen vector chart.
If you already have a C-Map Vector chart for your area and have it unlocked on the TZT, then verify the following setting: Go to MENU, then select S-52 DISPLAY, and from this menu verify that INFORMATION AREAS is set to ON.
It should display the 3 mile EEZ line (dashed line)
However, the chart will not display any type of text telling you that its the 3 mile EEZ line. But the TZT9/14/BB should display this chart information on a Vector chart.