If memory serves (someone check me on this). . .

You find the Striker in (SPOILER)the Cave on the Veldt in the World of Ruin, where you rescue Shadow by beating the Behemoths. So far as I can recall, it's not hidden or anything, just open the chests you see and you should come across it eventually.

Upon (SPOILER)leaving Shadow to rest in Thamasa, he'll run off eventually and do his own thing once more. It's at that point you'll want to bet the Striker and beat him so he'll join your party for good.