From memory (other should be able to confirm) a Torsen diff will spin the rear wheels in opposite directions when the rear is on a jack. So it sounds like you have a worn clutch type LSD. It should be a G series, Hilux diff.
Try calling a few diff shops and seeing what bits they have, and what they can do to a Supra/Hilux LSD , but unfortunately given you don't know exactly what is in there I reckon you'll just have to pull the centre and take it somewhere to discuss.
Bookmarks