Wohoo, I replaced it with a new switch and the light works now! Thank you all for your help. Not going to lie, I did felt a sense of accomplishment.
I have two quick questions though as I feel I may have done bit of a botch job...
1) Look at this poorly drawn picture.
A = what the ceiling looks like. The north and south holes are where the already existing screw holes were. The hole with the orange lines is where the electrical wires was coming from.
B = what the switch base looks like. The north and south holes are where the screw holes are. The square in the middle is where the cut out is.
Unfortunately because the cut out is in the middle, I had to pull the electrical wires over and 'squash' them under the switch cover and as such I wasn't able to screw the base flush with the ceiling; there is a several mm gap for example. Should I be worried about the squashing of the electrical wires and something like moisture seeping in from the shower?
In hindsight now, maybe I can just cut out more of the plastic. Perhaps I should do this or is it not a big issue?
2) How important is it that I cover the exposed wires with the sleeving seeing I won't ever touch it again unless I cut off all electricity from the circuit breaker before I open it?