What should I check?

The right blinker works normally. The left blinker runs fast, like a bulb is out, but there is no bulb out. To confound matters even more, when the headlights are on and I press the brake, it ceases blinking altogether. It will start blinking hyperactively again as soon as I release the brake.

 

There is a faulty ground somewhere. Most likely from the tail light area.

 

^this.

 

check int he trunk area there is alil harness for the bulbs int he rear and they tend to short out and cause this to happen. turn the blinker on and play with the wires. im sure u have a short back there i had this problem with my 97 sedan i went to a junkyard and grabbed a new rear bulb harness.