The light switch, radioclock, and climate control have terminals that are hot at all times with the key off.
Could be any of these shorted out.

I know this thread is quite old, but I thought I'd update you guys on what I think it might be...

I'm going through my dash, trying to figure out why my power door locks and power seats aren't working, and why my car chimes like the lights are on, with no keys in the ignition... so.. I found a second unit connected with the twilight sentinel... and it was quite severly melted... it is below, to the right of the column... and the plastic housing was extremely melted, and the heatsink for the diode was so hot, it desoldered itself from the board, along with the diode itself.. the circuit board was burnt beyond repair... like I said, I'll post pics when I get home..

Yeah, when I seen it, all I said was ***t, f**k, d**n... it was really scary seeing it... if I had a USB cable for my camera with, I would have posted pics, but, later tonite when I get home I'll show it... I got some good pics...

Ok, here we go with some scary pics..

















Well, there you have it... I thought you might be able to see the disoloration on the heatsink for the transistor, but the camera didn't get it at that angle... but yeah, that is incredibly scary... I thought of this thread as soon as I seen that box...

It is the Twilight Sentinel Module.. and the transistor overheated, I would think because of them using a piece of tin for a heatsink instead of aluminum or something more conductive...

Oh, and for the record, it is located below, to the right of the steering column, behind the metal cover under the column, hence why I would think that the plastic cover panel stayed in-tact..

I had a TLS that looked like that!
Made a real nasty smell too, But luckily I had a spare to change it out.

this car in the thread, doesnt have twilight sentinel...

thats not a TSM?
pretty sure that is it- I've replaced enough of them.

ohhh boy! thats freaky...i have been smelling some burning plastic smells from underneath my dash....i REALLY hope that doesnt happen to me....that would not be too fun...but if i keep smelling that, what should i check specifically?