That sounds like the switch connections you have just quoted again rather than the light connections.
There should most likely be 2 x twin & earth sheathed cables at the light fitting with the 2-reds connected together in a seperate connector, 1-black and 1-red in seperate connectors which are across the element of the light (bulb) itself .... one of the 2-reds that are connected together is the live cable down to the switch, thro' the switch and back up as the switch wire (normally comes back up as a black wire and you put a bit of red tape on it to distinguish it from the other Nuetral wires, but you say both the wires are Red at the switch)
The bare wire cut back is the earth which should be connected to all other earths and sleeved in green/yellow sleeving especially for any outside fittments
If the above is what you have then another cable will have to be run from the existing light to the new outside light (red connected to your 2-reds at the original light and the black to the black nuetral wire at your original light and then a twin & earth cable down to the switch from your new light to provide your feed / switchwire across Common and L1 of the 2nd switch. Again the 2-reds together in a seperate connector and the 2-blacks you have left are the Nuetral and Switchwire which will be connected across the light element
There are umpteen ways of doing what you require but this is probably the easiest.
Breezer ...I've seen you post a few images of this wiring in previous posts, do you still have them?
If it is a PIR security halogen flood light you are fitting you would probably be better forgetting about the 2-gang switch and coming out of the 3-pin socket to a switched fused spur unit (3-amp fuse) and up to the new light
Probably as clear as mud...