2007 Malibu: Problem with weird-acting turn signals and brake lights

This problem started when I activated my right turn signal and it was flashing
quickly, but my left turn signal flashed normally.  Then the next day, it
switched - the left one flashed quickly but the right one was normal.  Later
that same day,  it changed again and they both flashed quickly, and it's been
that way ever since.  The front turn signal lights are flashing quickly, but the
rear turn signal lights are not activating.  I replaced the rear bulbs with the
correct two-filament bulb, but no change there. Then I noticed that when I
activated the brakes, only the center bar on the trunk was lighting up - the
brake lights on the left and right are not activating.  Any idea on what might
be happening here?