Electrical issue with the four wheel drive

I bought this vehicle knowing it would be a challenge. The four wheel drive never worked, and smog issues became a priority. I solved the smog issue, but lately I have noticed on the four wheel drive light there is a. Button below for low range it is not on. If I push the four wheel drive button the light will get dim but will not go off until I turn the ignition off. When I do turn the key to the off position a light on the panel next to the right blinker light illuminates. I have noticed that it progressively gets dimer. The light is so low it is noticeable during the day. I know very little about four wheel drives. I do know the previous owner was not the type who rarely used the four wheel drive, if ever. So with the four wheel drive lights coming on and not going of, if would start with electrical vs mechanical. I have heard that lack of use of the four wheel drive can result in corrosion at contact points at the actuators. I really do not know where to start. I just hope I picked up this faster than I did with the emissions on this one. Thanks for any suggestions as to where to start.