Fuse 2 is actually the fuse from the regulator to the battery (see schematic below) - so if it's blown then you are not charging the battery.
Put the correct fuse in - if it blows again, you may have a shorted regulator.
Unplug both connections to the regulator:
With your test meter set to 'ohms' check in turn between each of the three yellow wires in the 3-pin connector to both the red & blacks in the 4 pin connector (the two reds are already connected to each other, as are the two blacks). Also check between the reds & the blacks. None of these should readings be 'short' (zero ohms).
Inspect the wiring at the three-pin connector - if the bike's harness looks charred/burned that is a sign the regulator has shorted. There is possibility it could have taken the stator with it.
Incidentally, the cable that plugs into the three pin connector - that should be a replacement auxiliarry harness: the original was deemed too small gauge for the job & was replaced with the auxiliary one as a recall. You should find that cable is stand-alone from the main bike harness and you can follow it back to the stator output connection. At both ends you should find the connectors of the original harness that is 'laced' into the complete harness. If you do not find that auxiliary harness, you need to get it. You should be able to get it at no charge from Triumph if the records on your VIN show it was never supplied.