On my 2001 Oldsmobile silhouette mini-van, the right turn signal works fine, but the left rear turn light alternates with the left rear brake lights (the fronts are fine). Then, if the brakes are applied with the left turn signal, the flasher flashes more rapidly and the left rear turn bulb alternates with the left reverse bulb in sync with the rapid flasher. Any ideas?

I had the same problem... the lower tail light bulb was in backwards... apparently causing a problem in the circuit... make sure the bulbs are installed in the same direction as they can be put in incorrectly and you won't realize it. Hop it helps

I've also seen the bulb's filaments broken and cross-shorted inside the bulb that caused some screwy lighting issues.
Inspect all the bulbs and their sockets as well.