Cracked Toothed ring on the offending wheel
the teeth may just be crudded up with grease/brake dust, worth checking.
the toothed cog could be cleaned with brake cleaner and a straw if you struggle to get at it. (some pound shops do brake cleaner aerosol cans and you can use the straw from wd40 to direct the spray)
reversing lights are not part of the mot

depending on the mot tester.... some pass the brakes anyway as long as they stop the car with good readings

allegedly ,other tricks include sticking black tape over the warning light or removing the bulb

not me Guv
