I want to add a 2nd security light to an existing light switch.

There are 2 wires (light brown & white? ) going into the back of the switch.

When I hooked the new wiring to the 2 screws on the side of the switch the new lights only operate in the "Off" position and the existing lights now also come on in the "Off" position but are very dim. The "On" position only operates the existing lights at their full power.

The two wires going to a switch are not hot and neutral which is what I guess you thought you had. The first wire coming to the switch is hot 24/7 and the other wire becomes hot once the switch is thrown. Is there another wire passing through this box too? Where do you live, what country or state?