The front brake light operates the light so you know the bulbs is working.
It's now easy to check for the rear operation without removing a thing
1) Open side panel as the large pic above shows.
2) Turn Ignition switch 'On'
3) Short the top two terminals together (the pair with the screws holding the wires onto the switch) with a wire or even a large flat blade screwdriver can be used to bridge them.
If the tail light illuminates all is well with the wiring loom to and from the brake light. Suspect the switch is dirty/unserviceable is some way.
No illumination? Suspect a wiring fault.
Most likely cause is just a dirty switch as the front end is open to the elements. Very easy to sort out though eh? WD40 and a good few push/pulls will do the trick probably