my rear wiper stopped working on my MK4 fr
take the plastic trim off the inside of the bootlid and have a fiddle with the wiring
the multiplug on mine came loose, pushed it back in work fixed
and rear wipers arnt part of an MOT, some cars thesedays dont have them
(some new BMWs and AUDIS to name some)
rear wiper is not part of the MOT i have just come back from having my ibza MOT'd
another interesting thing it that the spare tyre isn't part of the MOT either

