Triumph has common problem that ignition lock wires can bend so much that they finally get cut completely. One cause is quite short wiring and another is wire holder near the headstock. This causes 90degree bend to the wires when steering is at the right lock. When steering is a left lock thr wires are almost straight. One modification is to remove the wireholder so the bend is smoother at right lock. Overal design is flawed. I personally like ducati style steering lock/ignition lock which is located behind the headstock, so wires are not moved at all when steering is used.
If you just solder the wire where it has been cut, it’s not going to last, I soldered new wire to the old one, and pulled new wire to the loom and soldered the new wire to the ignition lock bottom, and other end was soldered to the old wire near the connector that is stationary under the tank. This way it holds up.