My 'guess' based on your present troubleshooting is that you have a partially shorted wire in the wiring harness.
Removing the fuse stops the problem, therefore the problem occurs after the fuse. Unplugging the BCM and the window motors doesn't stop the problem. Therefore the problem lies between those points.
I had a 2004 when Titans first came out, I don't know if I can find the electronic version of the wiring, but I will look later today. But, if we assume only the BCM and window motors are on the circuit, the only thing left is wiring. Your friend with access to the wiring diagram may have the wiring harness layout that shows routing for the wiring harness and location of connectors. That will give you a start as to where the actual wires are. The next step in the process is to physically inspect the wiring harness after the fuse as it wanders through the chassis (pull carpet and trim to expose the route).
It sounds as if there is a resistive short (hot wire to chassis) that conducts for a short period of time then opens, shorts then opens, etc. If it were a complete short the fuse would blow - the solution becomes much easier, find the burnt wire and replace. For now you need to look for a discolored wire (or wires, as the short may be between the hot and a ground wire) somewhere in the wiring harness - not a simple or easy task.