Thanks for the update Banksy I'm sure it will help other owners recognise some positive places to look should they encounter similar problems. Glad your sorted
Forget all the suggestions to change this or replace that. Problem is the CPU is set too high and unless battery is fully charged or you jump start; just click. CPU cannot be adjusted or re-mapped. Solution is to put a toggle switch on headlight. Turn headlight off when starting. This allows more voltage to start. Unlike other bikes, the headlight is on during starting, which draws enough juice to make the CPU stop the starting process.
Ignore the theories. Long story short: I had the click problem and figured out why and how to fix. Problem is electrical design flaw in Triumph. Too much juice is drawn from battery at start because headlight is on during starting process which triggers CPU to abort and you get the "click" even with a good battery. Install a toggle switch on headlight so you can turn headlight off when starting. That's all I did and now my bike is 100% dependable and no more click.