Hi barbarosa,
I believe the Gear Position Sensor ( Part Number T1290660 ) was updated,
but that is only from comments made by other Forum Members,
I have no personal knowledge of this.
I do know that your Dealer is WRONG to say the Fuel Tank needs to be removed
to replace the Gear Position Sensor !
The Gear Position Sensor is located on the left side of the engine
just forward of the gearchange input shaft.
The Service Manual describes the process thus :

The "Gear Linkage Cover" is held in place with one bolt at it's forward end,
which becomes accessible after removing the Fairing.
It's a fair amount of work to remove the Fairing just to uncover that one bolt,
but is not a difficult job - See this Topic if you have not removed the Fairing before :
HOW TO: Remove the Fairing .......There are also two pegs that are held in rubber grommets at the rearmost section of the panel.
After removing the bolt the cover will pull away to become free of the grommets.
With regards to DTC P1577 ( "Brake switch 2 correlation error with brake switch 1" )
check to see whether both brake switches ( front and rear brakes ) are working,
or whether one fails to cause the Brake Light to come on.
The most likely cause of the DTC is a faulty Brake Light Relay,
so I would try changing it for a new one,
assuming there is no obvious damage to the front or rear brake switch wiring.
The Brake Light Relay is underneath the Right Side Panel,.
It is a light blue colour and is the same type as the two Relays used for the Screen.
( Part Number T2506035 ).
You could try temporarily swapping the Brake Light Relay with one of the Screen relays
to see if this allows the DTC to be cleared.

Any authorised Triumph Dealer can obtain the Gear Position Sensor and Relays,
or you can check places like eBay using the Part Numbers quoted,
or order them from
"World of Triumph" in the UK - there will obviously be additional shipping costs to add !
Let me know how you progress with the investigation !
Cheers

