Buy a new tyre winch.
Everybody has replaced the spare tyre winch; well it seems that way, and if they have not, they just do not know that it does not work.
I purchased my new genuine one from BP Utah and for once, replacement is a clean hands not too difficult task. The winches are effectively not repairable.
You just need a nice day and a clean surface to lay on under the rear and a metric socket - forget what size but the task is almost pleasant.
The newer winches may be an improved design however once you have the new one installed, do not let the local tyre shop use their impact wrench on it to suck the spare back up. If so, you will at least be more experienced the second time re replacement.
2005 LR3 HSE 4.4L V8 petrol; 18" x 10 spoke wheels; Traxide dual battery kit; Rear Cargo area LED lighting; PIAA 2500K H11 Yellow Ion fog light bulbs; Patch cellular antenna to underside of interior of glass roof; Air Suspension ECU Fuse 35P disconnect switch; CounterAct LT-2 capacitive corrosion control system; LLumar AIR80 Blue Low E clear Infra Red heat reducing side window tint; Manual upper rear door cable release; Schrader valve "air in" mod to OEM air tank; Akebono ceramic pads on OEM solid vented rotors.