Welcome to the site !!
I have a few questions and a few suggestions , is this a U.S. bike or Euro ?? as wiring is completely different for each , and what Relay specifically are you referring to that burnt ??? , could it have constant power due to the wiring up the Trail Tech setup ?? , since the US models do not have the dual sport setup stock , they do however have a stock tail light so that wiring should have remained the same , was it changed/altered because of the Trail Tech kit ??? , it so then how it was wired is most likely the issue , and if you go back to ground zero on the wiring and start from scratch , I think you will locate where it is backfeeding the system and killing your relay , and most likely why you do not have a tail light without adding it to the headlight circuit
If you have a higher output Trail Tech Stator , then it should handle the extra output of the lighting kit , and for the most part if you are using a stock headlight bulb , the OEM stator should handle the added kit , wiring the taillight to the headlight circuit should not be a major issue , however , you should have been able to leave the original taillight configuration intact and just added the brake switch and light , which should only be going to the battery (thru a fused circuit) , or to a ignition switch (thru a fused circuit) , so brakes should be completely separate from the taillight system , regardless of who's kit it is , the headlight switch would only separate the stock wiring , which would be both high and low beam tied together , the "kit" simply separates the high from the low beam .....
What I think you need to do is go back to OEM wiring for the taillight , then as you add the dual sport system , make sure you are not connecting to existing tail light circuit causing the backfeed ......... it sounds like you have power where it should not be , so go back to the beginning and step by step add , and you should be fine , if the relay was OEM Honda than it has to be on the bike , but you need to omit the aftermarket stuff from tying into it , as that is most likely why it is constantly hot ...