Tsuki the Lunar Wind
Well, first of all: Archer is the name of one of the Rocket Executives in Gold/Silver.
Your background kind of jumped from "Oh, I like Jhoto" to "and my dad's an ex-Rocket".
On that note, how did your father become an ex-Rocket? I would assume most are Rockets for life.
Besides that, your background doesn't really tell me about why he's the way he is. There's nothing to suggest where he got his personality from. I mean, he came from the city with the Celadon Department Store and Erika the Gym Leader. Not to mention the Game Corner. There has to be something there, right?
Also: If his brother was completely happy taking his journey, then why didn't he want to take his? Was there a specific reason? Did he really have his "Rocket ideals" already? Most Rockets want to gain power and dominate the world, after all. And the League challenge is a great way to show commitment and skill.
(( I wouldn't recommend adding that he beat the Elite Four, though. Commander Blake was the Champion until recently, so you can't beat him without destroying his background. If you beat the first 4, then that's fine. ))
^u^ I like rounded characters~