Just the other day, I shut off the ignition and the alternator seemed to be giving feedback and kept the engine going (really low RPMs) for about 15 seconds. What are some common causes to this so I can check it out?

 

The alternator is not the problem. It doesn't run the engine, combustion does. What you are describing is commonly referred to as "dieseling". It is caused by the combustion chamber temperature being high enough to ignite the fuel even with the absence of spark. Check your base timing, something as simple as bumping up one grade of gas can help. Some carb's use a small solenoid to shut off air when ignition is shut off, you will have to check that out.

 

There are cases where the alternator can keep the engine running after the ign switch is turned off, but that would be the result of an electrical modification that inadvertantly tied the two ign switch outputs together that normally isolate the ign system power source and the alternator power source coming from the ign switch. If this was the cause, the engine would most likely continue to run normally when the ign switch was cycled to the off position.

 

Tim, the only way I see that happening would be if someone put a jumper from the "BAT" lug to the "IGN" wire on the two wire plug. The sense wire when removed has 0 volts as it is a pickup and not a feed. Could happen if someone was trying to reduce wiring, although not a good idea.

 

One detail I didn't mention was that the engine was cold. I started it up after sitting overnight, and after about 30 seconds shut it off, in which case the engine wouldn't stop for another good 10-15 seconds at very low RPMs. I did hear some kind of air pressure sound when the engine did finally die, so I'll check out that solenoid. It hasn't happened since, though.
As far as wiring goes, I haven't gone near the steering column at all, let alone the ignition switches. I've added a couple small things here and there, but no modifications to existing wiring.

 

sounds like run on to me. check the timing and the idle speed. if its idling to high it will run on like that, trust me I know mine use to do it. its sounding more lke an engine problem than an electical one to me though. just my $.02