I just recently fixed the exact same problem with my 93 Explorer. Water was leaking around the driver's side rear window glass frame and running down into the alarm module. You will have to remove the interior trim panel in the back compartment. This is a pain in the a_s. Lots of screws and push-in anchors. You also have to remove the upper seat belt anchor. After you remove this panel, you will be able to see two modules mounted directly under the back glass window. The module on the left is the 4X4 control module, the one on the right is the Theft Deterrant module. You will likely see some rust on the brackets that mount the modules to the body. If you want to confirm the leak, you can have someone outside with a hose pipe and spraying water on the window and around the frame. The window is mounted in a frame and that frame is bolted to the body with studs in the frame. This will all be obvious once you remove that interior trim panel.
You could just tighten all of the nuts on the studs around the window. That might or might not work. But if you have gone this far, its easy to remove the window and replace the seal. You need to remove all of the nuts from the window frame studs. I used a chisel and a hammer on the inside of the window seal to gently tap and break the seal between window frame and body. Once the window/frame is removed, you can remove the old seal material. Pay attention to how it is routed around the window frame, so you can put the new seal back in the same place. Remove all of the old seal material, dirt, etc. from the window frame and the body of the truck. Clean it up good. I used alcohol to help remove the gunk.
Go to your local auto parts store and get a box of window seal caulk. It is a cord that comes coiled in a box. Take an old piece that you removed to get the right size. The smallest they had when i did the job was a little bigger than what I had removed, but thats OK, it will squeeze flat. Be sure not to stretch it as you apply it or it may be too thin to seal. I took a little roller and pressed my seal flat to keep from having to torque down on the window frame bolts to squeeze it flat. Don't roll too flat and be careful because the seal will want to stick to the roller. Put the window frame back in and check for leaks. Then you can put everything else back together. It really wasn't as bad as I thought it would be. I pulled the other side off just to check for leaks too. It wasn't leaking, but the frame was loose, so I tightened it. I did not replace the seal on the passenger side.
