I just installed the P3 onto my 2016 TS.
I did not find such a connector on the ST, and had to 'tap into the cycle's individual wires.
A lot of stuff had to come off, to obtain access to the wiring: Rear Seat, Rear Rack, Pillion Grab Handles. I 'tapped the wiring in the area of the "square box", that appears to contain the front seat "tongue" when the seat is locked in position. That area gave good access to all the needed wires.
You could use one of the three CS3's circuits, but why? 'Tap the brake light for B+, just as instructions show, and keep the CS3's circuit unused (for something else).
One more thing: One turn signal wiring (I think, the left turn signal wiring) was clearly distinguished between ground and "signal", a black and white wire. The other one presented what looked like two black wires. "OK, which one is the signal?!". Closer inspection will show one of the wires has a colored stripe, (I think, a yellow stripe). That's the signal wire. I found out after 'tapping the wrong wire first...