The symptoms you describe indicate a short somewhere. the following checklist may be the best places to look at first.
1. There is a cut out switch on the clutch control as well as the gearbox and side stand. Faults in these switches can cause your symptoms.
2. Also check the loom where it enters the back or your head light - this can chafe and create an intermittent short.
3. Check your battery connections are good especially the earth cable at both ends.
4. The ignition switch (inside the switch) has been known to short also.
5. also check the fuse box using continuity - not just a visual inspection. If these all check out OK you can try replacing the headlamp/ignition relay.
These are all inexpensive faults to remedy worth eliminating before replacing the igniter or ECM. If it is your ECM it would be the first time I've heard of that failing.

You problem is not unique but it is not common either. I hope you find this fault and then I think you ill be pleased with your Triumph. They're a great bike but I understand how this problem would be souring you experience.
BTW. I think your bike may be an 09 which was the first year for EFI.

Good luck.


Cheers, Richard
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09 America, Staintune Pipes, K&N, Breathe, Hagon Nitros, AI & O2 removed, tune 20184 (modified), MTX-L a/f gauge