After much time spent taking my carbs on and off repeatedly, going through every electrical connection, and replacing electrical components, I finally resolved my 'cutting out and stalling' problem thanks to a post on this site. Even the mechanic at a dealership was stumped. I hate paying someone to tell me he can't find the problem. I simply disconnected the THROTTLE POSITION SENSOR at its connection under the carburettor and all my troubles dissapeared. Triumph needs to send a notice to the dealerships informing them of the problem with these sensors so people won't be paying to have their carbs worked on when it isn't neccesary or have coils replaced that aren't bad.
I can't find the post where unpluging the sensor was mentioned, but whoever you are...thank you.
