Yes but the High and Low have nothing to do with the gearbox or position, that is the motor in the transfer case. That's working as it should, in Low it will always display Lo and the gear you have selected (except your not displaying gears), in High it will display Hi for a few seconds then that goes out and it just displays the gear you are in.
What lights are you saying it doesn't put on in N or D? Reversing lights? If that is the case, as you've already worked out, it puts the reversing lights on when the X line is grounded, irrespective of what state the Y and Z line are in. If X line is grounded and the others are working as they should, P, R, 3 and 2, will display correctly, while D and N won't display anything (hence the select neutral warning when you use the range change) and 1 will display as 2. Are you sure the leds next to the gearlever are all displaying correctly in every gear or only some of them?