well, wouldnt hurt to open it up and look anyway, because it (shift motor) not working can be the result of either engaging or not engaging. where ever the worm gear and dial inside happen to be when it gets gunked up, well, thats where it stops. check it out, especially the springs and contacts on the armature.
as for the lights goin out on the dash, but it still be engaged.....could be the 4wd computer. its located behind the driver quarter panel (where the jack and the tire iron are located). there is a test you can do to the computer by pressing a white button, and watching the LED blink, but i forgot which is which (blinking light verses continous light) im pretty sure that if it blinks, then the computer is fine, there is something wrong with either the switch in the dash, or the shift motor. if the LED stays on, then the computer is malfuntioning. i think this is how it goes.
or it could ne the switch in the dash, but i highly dount this. but, still a possiblitly.
i really think it is the shift motor, because tapping it does not always work. when mine went out, i took a hammer and beat it, but it still didnt enage (yours would be oppisite) but thats my knowledge about it, maybe someone else will help ya out on the computer test.
peace, and good luck