Sure, but the 3rd brake light and the ABS are connected as part of the same circuit. The turn signals and the brake lights aren't part of the same circuit in any way except that they share a rear ground connection. My bet is on an issue with the rewiring on the right hand rear brake light.

@3bears You have concerns that it might be an issue with a bad LED. Since it is only the right hand turn signal indicator which lights up when you hit the brakes, swap the LED's from the right hand lights to the left hand lights and the left hand lights to the right hand lights. Swapping all 3 from one side to the other and then seeing if the left hand turn signal is the one that comes on when you hit the brakes should either confirm or rule out the LEDs as the source of the problem. If it follows the LEDs, then it's a bad LED, if it stays, then double check the wiring work you did.