A wiring question from a novice.

[only_sleeping]

I have a two gang two way switch, where only one switch has ever worked.

The switch on the left controls a light in the hallway, this light is also controlled by another switch elsewhere in the hall.
The switch on the right should control an outside light - it's not worked since I've moved in to the house though. I'd like to fix it now.

I've taken the faceplate off to have a look at what the issue was - I was hoping for a loose connection - but am confused by what I'm seeing. I was expecting to see a bridge between common and common, but instead there's one between common and L1. I've also noted I have two shades of brown wire (is that even a thing? It feels like it really shouldn't be a thing!) and on the left, the darker brown goes to common, and on the right it goes to L2 - marked with a red dot on the photo. Does this look okay or is there something visibly off? Thanks.

 

[foxhole]

What type of external light? I would suspect a failed fitting before a switch problem .

 

[only_sleeping]

What type of external light? I would suspect a failed fitting before a switch problem .

It’s a bog standard outdoor light from a diy store. I actually replaced it a few years ago for cosmetic reasons at the request of my wife - its predecessor didn’t work either, which is why I suspect it’s not an issue with the light itself.

 

[foxhole]

It’s a bog standard outdoor light from a diy store. I actually replaced it a few years ago for cosmetic reasons at the request of my wife - its predecessor didn’t work either, which is why I suspect it’s not an issue with the light itself.

But is there power at light when switched.

 

[only_sleeping]

The light doesn’t turn on and its predecessor didn’t either.
I don’t have any equipment to test whether power is getting to the light though.

 

[foxhole]

The light doesn’t turn on and its predecessor didn’t either.
I don’t have any equipment to test whether power is getting to the light though.

Then you don’t have what’s required to assess the problem.

 

[SUNRAY]

I think I show where each colour forms a cable
Green being a 3C&E to the other switch of a 2 way system
Yellow being the Live supply to the switch
Purple being a T&E switched live to the halllight that works

To that point it seems to be appropriate. Then it gets a bit tricky to see the cable sheaths and where these go in the top left corner so points to a blue wire:

Red being a 3C&E to the other switch of a 2 way system
Grey being the a T&E switched live to the outside light that doesn't work .

I see several scenarios, so I'll require more information:
Can you confirm my coloured arrows do indicate wires froming a cable, particularly Red and Grey, I've numbered them to help you correct me

What cable do you have at the outside light? T&E (brown/blue) or 3C&E (brown/black/grey)