First of all you don't want to rewire anything! This is why the other lights are flashing. Secondly is the bulb dual power or single? If it's single power you don't need to worry about the polarity. Just plug it in and go. And since you are putting leds in the turn signal you only need a single powered bulb. But it should stay lit. A dual powered bulb will not work in a single powered socket. And if it does it won't opperate properly. Do the other turn signals flash or light up?
Here is my LED brake/tail light. It's dual power.
I have a 2000 and the turn signals are factory led panels. So posting pics of mine won't help you any. How about turning on the hazzard 4-way signal? Does it flash or light then? You don't need to mess with any of the factory wiring. You're gonna end up like that guy I see on the road with turn signals for brakelights and reverse lights for turn signals and brake lights for.....well you get the point, haha.