Okay, I apoligize, Chris. Apparently my step dad and I both remembered wrong about the starter disengaging when pulling the switch.
We went to use the test light like you were talking about. Everything seemed to work normal. Light would go out when it was supposed too and get power when I tried to start the car. So, we hooked it back up and started it. After a few tries the starter stayed engaged. We pulled the wire and the starter still stayed engaged. We then disconnected the battery to get it to quit.
Now it gets interesting. With the wire still off, the key in the off position, and the clutch out, we went to hook the battery back up. The starter immediately engaged. So, it has to be that the solenoid is stuck, correct? That is the only place the starter can receive power from.
Our theory now is that the only place that solenoid can find ground, is through the panel it mounts on. Well, I was missing a screw, so just one was holding it on. Maybe it couldn't always find ground and was in turn looking for ground through the starter. We pulled the solenoid off and took it apart. It looks like the solenoid has been welding itself to each post, and I assume that happens when it can't ground itself to the

.
Does this seem possible? I guess I will get all the screws to mount the solenoid correctly and then slap a new one on there.