Alright, I read your OP twice now and hope I'm providing some assistance based on what I've done pulling my rack out and understanding how the system works. I'll try to explain it here as simply as possible, but bear with me;
Check your fuses, first. That's the obvious thing that prevents the sunroof from operating. If the knee panel fuse is fine, then continue.
The manual operation is as the guys mention - when you remove the light housing, it's a flat blade screw head which is LARGE and stands out. This screw is actually connected to the geared shaft which is powered by the motor, so you can get some torque on it to provide motive operation of the glass. Best bet is to get a geared electric screwdriver and find the biggest flat blade bit you own, and concentrate on keeping the bit centered in the slot while you use the electric drill to turn the screw. Go slowly, and determine which direction is the right way to open it. Don't force it. The gears in there are plastic and get angry if you try and teach them who's boss.
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You'll notice that in order for the sunroof to retract, it must first drop. There are links attached at the front and back of the glass track connectors which tilt down when retracting (*and up when closing, which seals the glass). These are plastic clips attached to the ends of the "pipe cleaner" flexible metal coil springs that move fore and aft to move the glass back and forth within the rack. The pipe cleaners use nylon bristles to center them in the tubes, brush dirt and debris out of the way, and hold grease to keep it moving smoothly. These coil springs form the linear teeth which interface with the 2 sides of the drive gear to move the flexible pipe cleaners back and forth.
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^ you can only see this part once the rack is removed, unfortunately.
This is what translates rotary motion of a gear to linear motion of the ends of the coil spring pipe cleaners. Look for damage to the small metal pinion gear teeth where the coil spring pipe cleaners run, as if they get out of alignment or jump their track, this can cause the middle of the metal gear to get worn down and slip it's teeth. The symptom of this is a sunroof that grinds when the controls are operated, but the sunroof may or may not move. The motor and electrical is working fine, but mechanically, the pinion gear is toast (*or, you've worn out the section of coil spring that sits here). Another symptom is that the sunroof glass closes, mostly, but one side may not lift into place to seal completely with the roof opening. It has run out of teeth.
The tubes which hold the pipe cleaner coil springs are L-shaped and go around the front and sides of the rack. Pay attention to the plastic clips which interface with the back edge of the sunroof, as these are the fastening points to motivate the sliding glass. If they're broken, you need new coil spring pipe cleaners, and the sunroof will slide by hand open and closed, because there's nothing attached to the motor mechanism. If one is broken, the mechanism tries to operate that one side, and it offsets the sliding glass and sticks open or closed. Symptom is that the motor binds up audibly, but the glass doesn't move, because it's getting cocked offset and bound up because it's only being powered on one side. This was the problem I ran into. The fix is finding a donor rack and pulling the coil spring pipe cleaner, tube assembly, and end links, and replacing your broken set.
Here is the attachment (*back) end of the tracks showing the plastic clips and links. Note that these are both tracks zip tied together for,storage. No, you can't have them. One is broken, anyway...
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Removal of the rack requires removal of the headliner, which is pretty staight-forward after you remove all the offending fascia and seat belt mounts. The headliner comes out the back cleanly and easily with 2 or 3 helpers to keep it from folding. Have work tables ready to set it on. The rack itself is probably 12-14 × 12mm bolts holding it in place to the underside of the roof. Conveniently, if you left your grab handles in place (*recommended), they will support the rack while you gently lower it out of position, so it can be chanted slihtly to slide out the back, once all electrical cables are disconnected. Note that the rain drains are exposed now, so inspect them closely and replace of they're torn or dry-rotted. At a minimum, grab a turkey baster and gently flush them out. This is also a good moment to decide if you want to add that 3rd row seat dome light fixture that's been sitting on your work bench for 5 years,...
As an interesting data point, the LX470 rack has an extra section of foam across the entire back edge which the LC80 did not have, and which seals the rack a bit better against the roof. Extra wind resistance for a quieter interior? Who knows. I didn't notice any interior sound difference, but my cabin is mostly occupied by gear whine from the transfer case intermixed with HAM radio static, so I got that going for me.
Installation is the reverse of removal! Haha,
I'm sauntered out to the garage and took those pics for you because I've got spare time, and can use the good LandCruiser karma, plus I didn't want the forum to lose this book that I wrote. Jeez,... it's 106F in my garage! Somebody owes me a beer,... cleaned up my post and put the pics where they belong. Good luck!