Easy check on the 4x4 light: unplug the 4x4 switch. A trim removal tool (or carefully applied butter knife) to pop the radio surround should expose the wiring. Note that this will not necessarily diagnose a bad switch, but should get the light to stop flashing. I'm not sure that a code reader that isn't the full-suite tool will read the 4x4 system codes.
Is it flashing in a pattern or just randomly?
Sure, give this a try, but my experience has not found this to be the problem on a door that is acting "always open" like OP's door. This has been my experience with doors that are acting "always shut"
I'm going to just take a hard opposition on this.
First, Your diagnostic procedure is for testing the opposite fault that he's experiencing. His issue is that the truck always thinks that a door is open, so your test has no way to differentiate between the door that is the cause being actually open vs. the truck thinking that now there are 2 doors open when a door besides the problem door being open.
Second, It's usually the wiring - it gets brittle with age and shorts to ground or gets corroded and too resistive to power. The place to start is the driver's door harness. Pull back the protective boot on the wiring in the hinge and look for cracked wiring. Then pull the drivers door panel off and examine the factory splices in the harness. You might as well check the switches while you've got each door/hatch apart to check the wires. If the drivers' door is not the problem, go to the rear upper hatch, then the lower hatch, then the other doors in the order of which ones look most used.