All the way back to the first 2 responses provided in this thread...

Something tells me that your brake lights are stuck on and what you perceive to be taillights coming on when you hook up the battery are your brake light filaments, not your tail light filaments. Then when you turn the lights on they get brighter because the 2nd filaments in the bulb all light up at the same time (as they should).

Have you checked and tested your brake light switch? Is it properly positioned at the pedal? Good continuity with plunger out? Open when plunger in?

Your turn signals sound like they could be directly related to the brake switch, or could still be ground issues, and they could manifest in grounding problems within the front turn signal lamps. Are the front lamps functioning?

Now that you have presumably good grounds at the taillights, do you have verified good ground straps between chassis and engine, and a solid ground between engine and battery?

As for chasing wires of odd colors and figuring out what they are, you need to use a multi-meter or at least a test light, and follow the conductor to see where it starts from. With your color description it sounds like someone before you may have attached a socket to the wrong wires, and you just blindly repeated the same error with a new socket. Or maybe a good repair was done simply with a different color wire at some time. Verify with wiring diagram that you have the correct wire, and verify again with multimeter/test light that the wire is live when it is supposed to be. It seems that you have a slightly hacked up rear harness and need to do some chasing to figure out why/how it's hacked.