Only third brake light is working

Fuses and bulbs ok but only the third brake light is working

3rd? Yikes, that means you'll have to take some trim off by the Left side - at rear - looking at vehicle - your left side.

The wiring harness to the upper Brake light seems OK, it works, but the harness has a branch that snakes down to the rear two lights so the wires to them are affected.

Do you have turn signal? Reverse - Backup Light, Running light - Rear Fog?

If no to those, then the harness from that rear left side back to the upper 3rd light will have to be traced back and see if you can find the break in their wires.

These harnesses offer ground - so even one broken wire can cause this - being ground or Brake wire itself.

IF you can get some help, have them press and hold the Brake pedal down so you can test with a voltage tester, to see if the lamps are receiving current - but no way to complete the circuit.

Thank you Handy Andy.
Done that and all seemed fine, harnesses and all the other lights. Then, for God knows what reason, I tested the bulbs for continuity and they've both failed despite looking good at first sight, filaments intact, only thing was a very faint light brown coloration on one side of the bulbs.
Replaced the bulbs and voilà, problem solved. But that left me scratching my head, and thinking what on earth caused both bulbs to go

Blown bulbs, but only in the back? None up front? Then consider yourself lucky. This may have been due to as simple striking a pot-hole or the car got bounced somehow, somewhere along your paths.

That when the lights were on; to cause the filaments to shake and pop like fuses when the filaments are white hot molten - it's possible even for the front headlamps to encounter the same problems - a bumpy road pops hi-powered lighting filaments by their hard shaking they receive in their housings.

Glad you got it fixed, you are welcome and go ahead and put in FIXED or SOLVED in the message header to help others know you found this solution...