The reason for her lack of truly attempting to convince Gawyn is easily explained: there was nothing in it for her. Note that, in KoD, she made certain to give more of the story to Mattin because she was doing her best to undermine Elaida as well as give Mattin the idea that she, as Amyrlin, could return his throne to him by ordering Rand to do it. When she has a vested interest in something, she gives it her all. When it's to help a friend, she is half-hearted in her attempts, at best.

A valid point. I guess I wasn't trying to say I don't understand why she would do something like that, but why she did in this instance when it was just as easy for her to explain convincingly as say what she did. I suppose the answer, as you pointed out and Cannoli has pointed out innumerable times, is that she is an arrogant girl with no regard for anyone but herself.