First of all, the tail/ brake lights are dimmer. Secondly, when a turn signal is on and the brake petal is pushed, the flasher speeds up and the signal shifts to the other side (left to right, etc.) What’s wrong?
I had something similar to this happening with a '94 K1500 Blazer I used to own. Neither turn signal would blink at all, and stepping on the brakes caused my instrument cluster and front turn signal lamps to light up (!!). I figured out that the wires to the trailer lighting harness had rubbed against the frame and were grounding out.
Have a good look at all the wiring going back to your tail lights, I bet you can find one that’s exposed and touching metal somewhere.
I suggest you check the grounding between the battery and the chassis. Clean the connections to see if that clears things up. If not, check the ground connection to the lights in the rear and clean that connection.