Ray is just a GOOD MAN isn't he! :2thumbs::2thumbs::2thumbs:
I'm not sure about the '03s so much, but I know that the later years of the EHCs are known to fail the same way "if" the headlight plug is corroded or melted or another high current load of that nature is bad. It's not that the two circuits are so much connected, but more like it suggest that the added current draw of the horn is tripping the main internal breaker of the EHC.
Check EHC connectors 1st!!! (mandatory)
Headlight - 5.5A (constant)
Starter Trigger - 10A (but this is not constant)
The next highest current load is the horn, and I'm not sure what it's rated to draw.
Then comes the ignition power connections I think
But Dielectric Grease works well on "every" electrical connection!