I bought my 1984 Eagle from a guy about two weeks ago. it's in really good condition for it's age but there are a few things that are wonky with it. The one i'm asking about here is the 4 wheel drive. It's stuck. Or bypassed. The guy was not really specific about what he did but it is now intentionally locked in 4 wheel drive. stopping the vehicle and switching the lever has no apparent effect. So far this has not presented any problems but I would like the option back.
Congrats on your new Eagle! From the factory, switching in and out of 4WD was a 2 step process, involving both the transfer case and the front axle. The only way I've heard to make it stick in 4WD is to wire up the arm of the transfer case so that it stays engaged in 4WD all the time. That would be the first place to look.
Many people eliminate the selection in the front axle by making it permantly engaged with a hose clamp, and you can find a couple thread on here about how to do that. This provides a "shift on the fly" option." So the previous owner most likely did this step also.
First, there were two options for the shift: shift-on-the-fly and stop-and-shift. It sounds like you have stop-and-shift, but please confirm 1983-1984 is a transition and AMC made it's updates running, not by model year. The switch will be labeled.
This determines the front axle assembly you have.
Once you know that, you'll need to assess any modifications you have. The front axle shifter, if equipped, may be locked and the transfer case may be held in 4wd with a spring or cable. However, it may just have had all the vacuum lines re-routed. In either condition you'll have to have rubber vacuum line, nylon air line, and an appropriate vacuum diagram before you start.