Have you done the headlight relay trick yet?
Triumph in thier wisdom decided to run the full power for headlights thru ign switch which causes it to over heat and wires fall of yo will find there a couple of threads on the subject there are two ways to fixing it 1 buy the Eastern Beaver kit or make your own using two relay or one the two relay method takes the power from headlight for switching only (very low load) and uses one relay for high and another for low beam, there is no other switches being put under high load and therefore gives max brightness to lights the I relay method still runs full power thru dip switch which will cause extra resistance and possibly switch burnout eventually. This is why the eastern beaver kit is also a two relay setup yet the tight wads at triumph have only now released an upgrade kit for lastyears roadster using a single relay, it is my opinion that I would rather pay for an extra relay and have the best power supply to lights