2001 Oldsmobile Silhouette problem with turn signals

My 2001 Oldsmobile is having trouble with the indicator lights. Here are the symptoms; When applying the brakes, the turn signals both glow faintly. When you turn on the left blinker it works fine when not breaking. When applying the brakes, it blinks at double speed AND the turn indicator at rear alternates flashing with the tail light. This alternating flashing does not happen on the passenger side. Also, with the left blinker flashing, the right blinker stops glowing when applying the brakes. With the right blinker on and applying the brakes, the left side indicator illuminates brightly, but not flashing. It glows constant until letting off brake pedal. And finally the left side backup light glows faint with brakes applied, then in reverse gear it glows bright, but the break light goes off.

If it means anything, about a month ago, I sliced into the left rear lights to hook up a trailer harness. Everything was fine until recently. I HAVE changed all 4 bulbs in rear left light assembly. Thanks!