Is the indicator on the dash just lit up all the time? Or is the actual turn signal lit all the time? If it is just the indicator, then it is probably a ground issue. I had the same problem on one of my samurais.....the dash indicator would stay lit all the time (but not with the key off).
If the actual turn signal bulb is staying lit even with the key off, then you probably have a short somewhere that is supplying constant battery voltage to the bulb.
