The housing of the front facing turn signal light that attaches to the front bumper is the ground for the circuit. If this housing is loose,or the screws that mount it are corroded the dash indicator stays lit...You may also have a failed head light on that side. The light may not be out in low beam,however, the high beam filament may be open. I recall that in a certain head lamp switch position, the high beam filament is the circuits ground. Try the housing ground first. I'd bet the ranch that this will be the trouble.