You don't need a converter. You need the correct turn signal switch. Sounds like your current set up, the switch controlled only the add on turn signal lights. So you first need the correct turn signal switch if you don't already have that. Eventually, you will end up with some wiring going to the back that won't be used, depending on which wires you want to use to power your turn/stop lights.
Then it will be power to the brake light switch, then brake light switch to turn signal switch, then the magic happens in there and out to the four corners for your lights. When you draw it out on paper, it looks like a spider.
