Hi Trev, yes using a relay, do not like the idea of 60 watts travelling through those little contacts.
Also, if the switch plays up or you break a wire, you can lose your lights, with the relay it will alway default back to Low Beam.
Trev, the reason I offer an alternative is because that looks like a DUCON ( red button and flipper ) to me and it is still possible to have the kill switch or the horn on the standard chrome button on the handle bars, I can not see the whole handle bar.
If the red is the horn button, might explain why the unit is on backwards.
Can not imagine having your kill button under your thumb is s good design.
I would suggest who ever put that unit on was not an auto sparky.