So much for accurate Manuels. There's a connector just forward of the transfer case on the left side that looks suspiciously like it goes in to the TCM (Transmission Control Module). Carefully pop it out, give both sides a quick spritz with WD40 or the like and reinsert. Try it again.
There's a thing in the manual about setting the cable up, but the sensors for noting what gear you're in are all inside the gearbox. Next step after this, if it doesn't work, would be to have that cable re-tensioned and after that, if that doesn't work, the TCM has to come out.
Removing the TCM requires emptying the gearbox of oil, dropping the sump plate and lowering the TCM out. There are two plugs on the side of the TCM (don't ask which side, I'll assume the left side since that's where the plugs go in). These apparently sometimes foul up as well. I'd say at this point, though, your car would be in a workshop somewhere and someone else is worrying over it.
Good luck!