Hello, sorry I'm late. Just skimmed the whole thread and I'll put in my two cents.
First, no eagles ever came with a posi rear diff, all eagles are open rear diff's. So, the previous owner either installed something aftermarket or possibly even a whole new diff out of a jeep. Or, on the worse side, there might be some seriously rusted/mangled rear end parts. I've seen it happen once or twice when someone goes 4X4 ing and gets water in the diffs and then let's the car sit. Doing so rusts the Carrier solid. But I've only seen that once or twice and only on cars that have been sitting for years.
Still, if I were you I would pop off the filler plug and see what the fluid looks like, just to be safe.
The dual exhaust is also interesting to me, as there are no dual exhaust aftermarket kits available for the eagle, and nothing stock either. Whatever is under there is completely custome and obviously quite expensive if the previous owner didn't do it himself. Be wary of that as well.
As for the parking brake, you are correct. You cannot buy a new cable for the eagles. That said however. Almost all of my eagles have had seized e-brake cable's and I've reconditioned them all. It just takes time, patience, a lot of WD-40 and sometimes, some good ol fashion FIRE!
And as for the water leakage. Not good mate. There was one eagle(whuntmore can chime in on this) that belongs to a member on here that had a similar leakage problem, now I can't remember if this one your talking about now is the one without carpets or not, but long and the short of it, hiding under the carpet were no one could see it, the whole floor pan was rusted out completely. So be wary.
Now, the 4X4 system. I have fought for HOURS on numerous different eagles trying to get the stupid vacuum operated 4X4 to work. To be honest, it a very simple system. If it's shift on the fly(no tab to pull down to engage 4X4) there is only one vacuum operated actuator to control the transfer case. To engage manually, remove the transfer case skid plate (9/16's bolts) and use a 9/16 wrench(I think, it's been a while) on the nut holding the lever and push it towards the front of the car, you might have to have people rocking the car while you do this until you feel it engage. For a stop and shift it's a bit more complicated. For those there are two vacuum operated actuators, one in the same exact place on the transfer case, working in the same way. And another on the front differential(if you want i can into the specifics of why and such, but for now). The actuator on the front Axel engages and disengages the front Axles. So, even if the transfer case is engaged you won't get any power to the front wheels. Although you should also notice, if that's the case, that you have a lack of responsiveness and that the speedo will jump slightly before you take off due to there being more power going to the front shaft, hence it spinning faster than the rear.
If you have an understanding of were some of the vacuum lines go, what pull vacuum and what requires vacuum. It is not an overly big job to re-rig your actuator system to be less tied up with the rest of your vehicle vacuum system and hence work better.
And Finlay, I'm assuming you've already done this but take a close look under all of the plastic skirts around the fenders and covering the rockers for rust. About two years ago i bought a beautiful SX/4 for a not bad price. Not a hint of rust anywhere under the car or anywhere else. It wasn't until a week or so later, when i had it up on a hoist and poking around with a screw driver that i found both rocker panels were completely gone. Rusted clean through. After i was done with the screw driver, had the carpet not been there I would have been able to fit my arm through the hole all the way up to my shoulder. It took weeks of very extensive surgery to get the car to pass safety. Just consider yourself warned.
Sorry about the long post.