Welcome
@GeordieBear - although you list location as Glasgow, from your screen-name you're from Newcastle maybe?
Note that there was a recall notice on the alarms - not sure if yours fall into that affected group - details here -
OEM Alarm Safety Recall
The Main Harness alarm connector is under the tank, about half-way back on the right side - there should be an extender harness from that connector, to a similar connector that plugs into the alarm module
It would be best to remove it at the main harness connector and remove the extender along with the alarm module.
You may find that there is a large heat-shrink sleeve over that connector set, so you may have to slice that off before you can decouple the connectors.
You then need a bypass connector to plug into the Main Harness side - that has two bypass loops that complete the interlock circuits - your bike will not run without these.
You can check with your Triumph dealer to see if they have one (if you can reach one of the mechanics directly, good chance they will have one removed from a bike)
If you can't get it, I can explain how to cannibalize your extender harness to make one (or source the connector and terminals to make new one)
I could make one for you, but the cost & time to get it to you makes it bit prohibitive since I'm in US