I wasn't planning on arguing, I was just curious how it would work.Heat Wave is a wave of hot air blown at the target. Dazzling Gleam is sudden burst of light. The two moves are essentially the same thing, just with different forms (Heat Wave is heat, Dazzling Gleam is light). This seems like enough to make it seem like it should work.
Also, I've seen refs get away with referee's judgement decisions like that on a weaker argument, so you may as well not try to argue.