When you go to Stark Mountain you will meet your rival (you won't battle him/her). After that you will be able to face him at the Fight Area on the weekend(Not on Friday).
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if you mean after the elite four,after you beat the elite four,go to snowpoint city(the one with snow)take the boat to battle area,then, every Saturday and Sunday, he's just outside the battle tower.
To get the National Pokedex, beat the Elite Four.
I do not know where he is after beating elite four soul silver. I hope to find him soon.
you get it after you beat the elite 4 go to the desert and catch one.
Yes, that's true!