So, I seem to have a bit of a problem with my 93 STS.

As soon as my head lights come on automatically at dusk, my car tells me my signal light is on. My right arrow remains lit on my dash, even though I know the turn signal is not on.

The "Turn Signal On" message only happens once the head lights are on. Then, when I signal left, the hazzard light flashes.

This only happens at dusk or when the head lights turn on, never during the day.

During the day, my right turn signal flashes faster on the dash, I assume alerting me of a burnt bulb (however by looking at them, I have no idea where to start - they look fine to me). But no dash message & no constant lit right arrow.

Any suggestions on what might be the problem?

You have a poor ground at one of the turn signal bulbs. It will "feed back" thru the dash indicator. If the same bulbs are used as brake lights, simply turn on the emercency flashers and walk around the car to locate the faulty bulb. Closely inspect that bulb and its socket. Most likely a corroded socket.

Thanks very much for the info.