ABS and Traction Control lights

The car listed above is a GTP, I couldn't select GTP in the dropdown, it has a 3.9 rather than a 3.5 in a normal G6. In the last few months, I have no idea how it started, my ABS and traction control lights will flicker after driving for about 10 seconds or getting up to like 15 MPH or 2,000 RPMs. My brakes are shaky and the pedal kicks back slightly if I try to brake before my lights turn on. Once the lights turn on and stay on, my brakes work fine, and I never have problems. I have done some research and I'm thinking it's my wheel speed sensors. I am not completely sure how these sensors work or even where they are, and I don't want to get started before I diagnosis the problem exactly.
I am attaching a video of the exact problem - I initially accelerate and brake right after I started my car, and you can hear the shaking and kicking of my brakes. Then, I drive for a couple seconds, the lights turn on, I brake again, and they're perfect.

Any ideas?