Bottom Line, here is something to check out. Worth a shot. It won't cost you anything but time:
I had similar electrical issues with my 02 xlt. The dome lights would stay on until the battery saver feature turned them off, the driver side puddle light didn't work, the keypad on the door would set off the alarm when I pressed it, the door ajar light would flash and beep at highway speeds, etc.
A lot of electrical issues can be traced back to broken/damaged wire(s) in the boot between the body and the driver's door. I found a broken wire and repaired it and all is back to normal!
Here is a great thread for removing the door panel,thanks to
borland for the awesome write-up:
http://www.explorerforum.com/forums/showthread.php?t=249253
Here is a great thread for checking for broken/damaged wires, thanks to
synyster for this awesome write-up:
http://www.explorerforum.com/forums//showthread.php?t=270081
I don't know if your issue is related to the keyless entry system or not. But, like I said, this won't cost you any $$ to check out.
Good luck and let us know how you make out.