I spent a bit of time yesterday looking at the wiring diagram for the KZ. The voyager manual is a supplement to the KZ manual. It's not very clear on the flow through the wiring in the circuit. At one point the hazard relay feeds through the ignition switch and trying to follow the flow, one must go to the section in the manual for diagnosing the ignition switch.
Your description says that you replaced the relay and can hear the relay clicking. The power feed for this circuit from what I see comes from the master switch energizing the orange wire with a green stripe. then the orange with green runs to the ignition switch and comes out on the orange wire to a 5 wir plug. as it goes through the 5 wire plug it switches back to a orange wire with a green stripe. Then through a hazard indicator switch coming out on a green wire and grey wire feeding the turn signals.
For the relay to be clicking, the circuit must be complete ie. the 12 volt feed must be completed to ground. Normally that would be through the light bulbs. If you have the clicking going on but no lights working, that would suggest to me that the circuit is complete but not through the bulbs. possibly a pinched wire and I would suspect somewhere shortly after the hazard switch since the circuit is only complete after selecting the hazard lights.
Hope this helps. Good luck. Electrical can be a pain in the a$$ sometimes.