Rather than use the tail lights, use the brake lights. With a 7 wire Signal Stat controller, you can run turn signals through the brake light circuit such that for example if you are braking and indicating rt turn, the left side brake light stays on full and the right side brake light flashes. This is completely independent of the tail light circuit which operate as original
So do I cut the right light wire and run the new wire to the light or splice the new wire into the existing wire that connects the two lights?Hope I have this right: You're correct in that the tail lights are wired in parallel. But so are the brake lights. One wire runs from the brake light switch back to the left rear light and loops over to the right rear light. You'd definitely want to use the brake lights, not the tail lights for your turn signal. And you'll need to run a separate wire from the turn signal switch back and across to the right rear brake light (you cut and splice onto the original brake light wire that connects between the two rear lights. That effectively splits the brake lights into independently-wired units for the turn signals.
So do I cut the right light wire and run the new wire to the light or splice the new wire into the existing wire that connects the two lights?