I got smoke from the steering column of an '89 Civic which turned out to be the ignition switch contacts being worn. That car had begun to occasionally start but immediately die, also. I was on a trip when I started getting smoke, so I twisted the "Run" wire to a +12V source, effectively bypassing the contacts which were worn. I would just untwist the wires to shut the car off.

I replaced the contacts after returning home and the problems went away.

Your problem could be all sorts of things, but ignition switch contacts are a good guess. -scott