CTS is Bosch style 2 pin connector. No pigtail, harness clips straight to it. "natural" color. In front of turbo area, in the crossover pipe portion of intake.
test if the idle issue is AAV related. Pinch the hose. If idle drops, then you're AAV is stuck open or leaking.
I've just capped of a few of them. Then set the idle with the screw in the back of the throttle body. Might mean needing a tad bit of foot throttle on very cold days to warm up, but otherwise works fine and is less annoying than a constant high idle.